Ch_2BranchiniB

Brandon Branchini's Wikilog - Period 6 CP Physics 2010 - E. Burns toc

Chapter 2, Section 1
11/6/10 Science of Sports Source: ESPN's Sports Science [] Summary: On SportsCenter, there is sometimes a segment that goes through the science of a particular sport; it is called Sports Science. It is great source to watch and learn about physics of sports, as well as, to see how tough or fast these athletes really are. The video shows the NFL superstar, Dwight Freeney. If you don't know, Dwight Freeney is the star defensive end for the Indianapolis Colts. This segment breaks down the physics of Dwight Freeney sacking a quarterback. First, Dwight Freeney tries to get pass the offensive lineman by spinning at a 90 degree angle. When spinning, he is only airborne for .30 seconds. He spins about as fast as an Olympic figure skater and he weighs 270 pounds! Freeney accelerates to 90 percent of his top speed, covering 7 yards, in just 1 second! Dwight Freeney delivers a hit of 2800 pounds of force.

11/8/10
 * What do you think? **
 * Figure skaters keep moving across the ice at high speeds for long times while seeming to expend no effort. They can do this because there is not a lot of friction on the ice and the figure skaters have a lot of momentum, which make them move quicker.
 * A soccer ball continues to roll across the field after being kicked because of the momentum of the ball that has been kicked. Once an object motion, there has to be an unbalanced force to come and stop it.


 * Investigate**

In this Investigate, you will use a track and a ball to explore the question, “When a ball is released to roll down track and up the opposite side of the track, how does the vertical height that the ball reaches on the opposite side of the track relate to the vertical height from which the ball is released?” Make a hypothesis. Answer the question to the best of your ability at this time.
 * The higher the track, the more momentum the ball is shoot up the opposite side

1.Set up the simulation and run the first trial. a) Press pause to stop the simulation. Note that the simulation ignores friction effects entirely. b) Check the box marked “Measuring Tape”. c) Use the default track and all other default settings. Use the measuring tape to measure the initial height. à 6.50 meters  d) Press Play. e) Place your cursor at the height point that the skater reaches on the opposite track. Measure the vertical height of this mark. 6.50 meters

2. a) Predict where the skater will reach his highest position if he begins at the same place as before. He will reach the same point as he did with the last one. b) Explain why you think so. This is because if you change the end point, he isn’t being dropped from a steeper slope, he is still being dropped from the same place, so his highest point would be the same. He has the same momentum, as he had before.

3. a) How close was your prediction to the actual outcome? Why do you think your prediction was “close” or “way off”? Our prediction was close. I think my prediction is close because I checked with the application and got the same answer as my prediction. b) Measure the vertical height where the ball stopped. Write a sentence that fully describes the movement of the ball in terms of its starting and recovered vertical heights. It would be the same measurement as the highest point. The vertical height is equal to the highest point, so if you drop the person from 6.50 meters, the highest point would 6.50 meters, and the vertical height would 6.50 meters.

4. a) First record your prediction. If you make the slope less steep, his highest point would become less, as well as the vertical height. b) Compare your prediction with the outcome. My prediction was correct.

5. Imagine what would happen if you changed the right-hand section of the track so that it would be horizontal (zero slope). a) No matter how far along the horizontal track the skater rolls, would he ever recover his starting height? Since there is no slope on the opposite side of track, there is no force to push him back up to his starting height. b) How far do you think the skater would roll? He would keep rolling until there was another force on the track. c) What would keep the skater rolling on a horizontal track? You would make the track as long as it can be. d) Try this on the simulation. What happens? He travels on the track, but eventually he stops because of the loss of momentum.

6. Conclusion Questions: a) What happens to the length of the opposite track the skater rides as the slope decreases? The length would increase. He would need to travel more distance. b) What happens to the final vertical position on the opposite track the skater rides as the slope decreases? The final vertical position on the opposite track would decrease because it would mean a wider slope. c) Remember that we are ignoring friction. The initial question was: “When a ball is released to roll down track and up the opposite side of the track, how does the vertical height that the ball reaches on the opposite side of the track relate to the vertical height from which the ball is released?” What is your answer to this question? If the slopes are the same on both sides of the track, then the vertical heights are equilivalent. But, if one side has a wider slope than the other, then the side with the wider slope would have a smaller vertical height than the other side. d) If the opposite track was infinitely long, and frictionless, when would the skater stop? He would never stop because you need friction to brake.

**﻿Physics Talk**

Summary: ﻿Galileo Galilei was an Italian philosopher, physicist. He introduced experimental science to the world and performed an experiment that we did in our investigation. He observed a ball that rolled down one ramp seemed to seek the same height when it rolled up another ramp. He also formed a law of inertia, which is defined to be the natural tendency of an object to remain at rest or to remain moving with constant speed in a straight line. He concluded that an object at rest remains at rest unless something causes it to move. He also realized that objects do not stop on their own but stop because there is a frictional force working. Sir Issac Newton was another famous scientist. Newton used Galileo's law of inertia as his basis of developing his first law of motion. Newton's First Law states that in the absence of an unbalanced force, an object at rest remains at rest, and an object already in motion remains in motion with constant speed in a straight-line path. He also explained mass, which is the amount of matter in an object, or tendency to resist a change in motion. He concluded that if their is more mass, there will greater inertia. The talk also takes us through the physics of a javelin throw. They explain that speed is the change in distance per unit of time and that velocity is the speed in a given direction. Acceleration is the change in velocity per unit of time (how fast your speed is changing). The total speed of the javelin is the sum of each of the speeds of the hand, elbow, shoulder, and body. They also explain frames of references. A frame of reference is defined to be a vantage point with respect to which position and motion may be described. In my own words, a frame of reference is the spot you identify as having a velocity of 0. Inertia is a PROPERTY of matter that measures the resistance to changes in an object's motion. MASS (kilograms is the base unit in Physics) is how we measure inertia. Weight is how much gravity pulls on a mass. Running starts increase ones speed and momentum.


 * Checking Up**

1. Inertia is defined to be the natural tendency of an object to remain at rest or to remain moving with constant speed in a straight line. It is a property of matter that measures the resistance to changes in an object's motion. 2. Newton's first law of motion concludes that in the absence of an unbalanced force, an object at rest remains at rest, and an object already in motion remains in motion with constant speed in a straight-line path. 3. An unbalanced force needs to act on an object to stop it from moving at constant speed. 4. A frictional force that we cannot see stops the motion of the ball. 5. Speed does not affect inertia. It would be the one with greater mass because greater mass = greater inertia. 6. It is important to establish a frame of reference when describing the speed of the ball because you need that vantage point to explain the motion.


 * Physics To Go **

2. The vertical height would also be 20 cm on the other side. 3. It is not possible to arrange conditions in the real world to have an object move, unassisted, in a straight line at a constant speed forever because of friction. We cannot see friction, but that force will stop the ball from moving. 4. The hockey puck will travel with a constant speed until he hits the wall because then it will change direction and gain velocity. 5 and 6. 7 and 8. 9.  10. a) Three sports include soccer, hockey, and croquet. In croquet, the object will remain at rest until you hit with your club (force). This makes the ball move in a straight line at constant speed until he hits a post. In soccer, the ball will stay at rest if not a single player touches it. When someone kicks it (force), the ball will move in a straight line at constant speed until another player touches it. In hockey, the puck will remain at rest unless you hit it with your stick (force). This will make the puck continue to move in a straight line until another stick hits it or the puck hits the wall. These three sports all support Newton's first law of motion.  b) Croquet Announcer: Terry gets up for his hit. He gets in position with the ball still at rest. He rears back and hits the ball. The ball is moving in a straight line, until..Oh no..It hits the post! The ball now is stopped, so he gets one more chance. Soccer Announcer: Henry is lining up for the penalty kick. He gets a running start with the ball at rest. He starts running, hits the soccer ball, and it hits off the post. This stopped the ball from moving in a straight motion and constant speed. He is out of luck tonight. Hockey Announcer: Pete is running to the puck, that is at rest, He then hits the puck, which makes it travel in a straight line. The puck shoots in a straight line until the puck hits off the wall! And now the puck is going in a different direction.
 * 1. a) The ball will keep rolling because there is no unbalanced force to stop it. **
 * b) Newton's first law states ** that in the absence of an unbalanced force, an object at rest remains at rest, and an object already in motion remains in motion with constant speed in a straight-line path. In this example, the object is rolling in a straight path so it will remain in this motion.


 * What do you think now?**
 * After reading this section, I can further analyze the questions asked at the end of the section. Figure skaters can keep moving across the ice at high speeds for long times while seeming to expend no effort because of Newton's first law of motion. The figure skater can do this because there is low friction between the ice and skater's blade. This means it will be easier for the person in a straight motion. A soccer continues to roll across the field because Newton's first law of motion says that an object in motion will remain in that motion at constant speed unless an unbalanced force acts upon. If you get a running start, gaining momentum and kicking a soccer ball at rest, the ball will keep rolling, until there is an unbalanced force stopping it from doing so. The starting speed and the speed they used when pushing off the ground determine the ice skater's speed. The running start to gain momentum when kicking the soccer ball and the actual speed of the kicked ball determines the speed of a soccer ball. They keep moving because of Newton's first law of motion which states that an object in motion will continue to move at constant in that same motion, unless acted upon an unbalanced force.

11/10/10
 * Inquiring Further**

Sources: scienceblogs.com/builtonfacts/.../the_physics_of_curling.php ; en.wikipedia.org/wiki/Slide_(baseball) 1. In curling, this is demonstrated when you push the stone down the ice to knock a stone out of the “house”. When the stone that is hitting the other stone it hits it knocking the other stone out of the house and then stops as it hits the stone and stays in the “house” giving the scoring team a point. 2. Baseball players run straight through first base because you barely slide when doing so. You slide when you reach second or third base to get to that base faster, so there is a less chance of you getting caught stealing.

**Reflecting on the Section - see group wiki**

**Chapter 2, Section 2**
**What do you see?**
 * I see a kid walking slowly on the top picture. The kid on the bottom picture running full speed because he wants to give the flowers to his girlfriend.


 * What do you think?**
 * 100 miles per hour is how you right the velocity of some pitchers in the MLB. This is almost impossible to hit, you need to react extremely quick to a pitch at this speed. 100 miles per hour is a velocity unit and relates to its direction. 45 m/s is another speed, but it is unusual to describe a fastball with using these units. Both these speeds are the speeds of when the ball releases the hand of pitcher and reaches the glove of the catcher.


 * Physics Talk**

When signs of V and A are the same, increasing speed and when the signs are different, decreasing speed.
 * Summary:** This Physics Talk explains how to measure motion. We learned that in constant speed, the distance between ticks on the tape is equal in length. We learned that for slow constant speed the ticks were closer together and when we did faster constant speed, the ticks were farther apart. We also learned about how to show acceleration, which is the rate at which velocity changes. Positive acceleration, when the person is gradually increasing speed, the distance between the dots got gradually longer and for negative acceleration, when the person is gradually decreasing speed, the distance between the dots got gradually shorter. They also review how to calculate speed. Some terms they used include average velocity, the rate at which distance is traveled, and instantaneous speed, which is the speed measured in an instant: the speed as the time interval approaches, but does not become zero. The difference between average speed and instantaneous speed is that instantaneous speed is speed at a particular moment, while average speed is average speed traveled throughout the total duration. They also review how to calculate acceleration, where you use the formula, change in speed/time interval.


 * Checking Up**

1. a) Constant speed show ticks that are equal apart. b) Positive Acceleration shows ticks getting gradually longer in distance between each other. c) Negative Acceleration shows ticks getting gradually shorter in distance between each other. 2. Average Speed = distance traveled/time elapsed --> Average Speed = 400 meters/50 sec --> Average Speed = 8 m/s  3. The difference between average speed and instantaneous speed is that instantaneous speed is speed at a particular moment (smaller time interval), while average speed is the average speed traveled throughout the total duration.  4. Acceleration = Speed/Time Interval --> 110/.0028 = 2.8 m/s^2

**Physics To Go**

1. Average speed is the average speed driven throughout the duration of the trip, while instantaneous speed is speed at a particular moment of the trip. 2. a) V = d/t --> 1 km = 1000 meters --> 1000 m/15 s = 60 m/s b) V = d/t --> 84 m/6 s = 14 m/s c) V = d/t --> 9.6 km/2 h = 4.8 km/hr d) V = d/t --> 400 km/4.5 hr = 89 km/hr 3. a) A runner falling down would indicate a negative acceleration. b) A runner taking off from a starting block would indicate a positive acceleration. c) In this instance, there will be no acceleration, as it is zero because you are walking at a steady speed. d) A soccer ball being caught by a goalie would indicate negative acceleration. e) A bowling ball at constant speed would have no acceleration. f) A parachutist falls at constant speed would have no acceleration. 4. a) A and D represent a student moving with a constant increase in speed. b) B represents a student moving with a constant speed. c) A indicates the greatest change in speed each second. d) C represents the motion of a student whose speed first increased but later decreased. e) A would have positive acceleration. B would have no acceleration. C would start out with positive acceleration then would have negative acceleration. D would have positive acceleration. 6. a) -1.4 m/s b) The acceleration has a negative value. 7. a) This is an object moving with constant speed. b) This is an object moving with increasing speed. c) This is an object that starts out with slow constant speed --> increasing speed --> faster constant speed --> decreasing speed, then goes back to the original slow constant speed. d) This is an object that starts out with decreasing speed into a constant speed then increases its speed. 8. V = d/t --> 100 mi/2 h = 50 miles per hour.  9. No, the average speed give you the average speed at which the driver drove throughout the whole entire duration, while the instantaneous speed is speed at a particular moment of the drive. Thus, the instantaneous speed can be greater or lower than the average speed.  10 and 11. see work below  14. a) People running a marathon may want to keep the same constant pace. b) A fastball moving at a constant motion with fast speed. c) When walkers walk around the block, they walk at a constant slow pace. d) A running back trying to outrun all the defenders. e) A car coming to a complete stop at a red light would have negative acceleration.

**Physics Plus** Rebounding = change direction --> Even if speeds are small, accelerations can be huge if the bounce times are tiny. 1. -100 m/s ^2 2. -5 m/s^2 Work: 3. The acceleration is constant for the entire trip, so it is linear. This means that it is traveling with an acceleration of -5 m/s in every situation.
 * Velocity || Acceleration. || Example ||
 * small || small || turtle ||
 * big || big || airplane, rocket, racecar ||
 * small || big || rabbit, dog, deer, rebounding (any object) ||
 * big || small || truck ||


 * What do you think now?**
 * 100 miles per hour and 45 meters per second are both measurements of velocity. 100 miles per hour basically means that for every hour, you will travel 100 miles. 45 meters per second basically means that for every second, you will travel 45 meters. In this case, velocity is defined to be the total distance traveled/time. The time intervals in both of these include seconds and hours. The distance are measured in miles and meters. You usually use these two measurements to measure different examples. You would use miles per hour to maybe measure a fastball or a speed limit. You use meters per second to represent a reaction time.

Chapter 2, Section 3

 * What do you think?**
 * A force is defined to be a push or a pull. Force is related to mass. So, since a bowling ball weighs more than a tennis ball, you have to use more force to get the bowling ball rolling. If you used the same amount of force on both, the tennis will travel farther than the bowling ball and also go much faster.


 * Investigate - see group wiki**


 * Physics Talk Pg. 160 - 165 t**


 * Summary:** Newton's Second Law equates the formula, Acceleration = Force/Mass or Force = mass x acceleration. When solving for force, you use the units, newtons. A newton is defined to be the force required one kilogram of mass accelerate at one meter per second squared. All in all, Newton's second law tells us that acceleration is caused by an unbalanced force. They tell us that where there is acceleration, then there is an unbalanced force. When you apply a force to an object with a small mass, then the acceleration can be large. If you apply a force to an object with a large mass, the acceleration can be smaller. Thus, the less the mass, the more acceleration and vice versa. Force and Acceleration have a direct relationship, while force and mass are inversely related. We use significant figures when wondering where to round to when a problem is solved. Some rules include: a zero between a non-zero object is significant, a zero at the end of a decimal number is significant, a zero at the beginning of a decimal is not significant, and a large number without a decimal point, the zero is not significant. For adding and subtracting, the final result should have the same amount of significant figures as the measurement with the fewest amount of significant figures. For multiplying and dividing, the final result should have no more significant digits than the factor having the fewest number of significant figures.

**Checking Up** 1. Newton's second law tells us that acceleration = force/mass and force = mass x acceleration. It tells us that if there is no unbalanced force present, then there cannot be any acceleration. 2. If you happen to increase an object's mass with a constant force, then the acceleration will decrease.

**Physics Talk Pg. 166-167**

**Summary:** ﻿This part of the physics talk explains gravity, mass, weight, and Newton's second law. Weight is defined to be the vertical downward force exerted on a mass as a result of gravity. As said in the previous part, Newton's second law states that if acceleration is present, then there must be an unbalanced force acting upon it. Using Newton's second law, you can use this equation to calculate weight: Fgravity = Mass x Agravity and w = mg. G is the acceleration due to gravity, which is always 9.8 m/s^2. They also talk about unbalanced forces and balanced forces. When two forces act upon something at the same time, the direction and magnitude of the forces determine the motion of the object. If the forces are in the same direction, then the sum of the forces will cause a larger acceleration than either force alone. If two forces are in the opposite direction, then the net force could be zero, thus there would be zero acceleration, also. A free-body diagram is defined to be a diagram showing the forces acting upon an object.


 * Checking Up **
 * 3. An object weighing 30 N basically means that the force is 30 N, as well. **
 * 4. If you were on a planet with higher acceleration, then your weight would increase. Your mass would stay the same. **


 * **Physics To Go

3. A = F/M --> 42/.30 = 140 m/s^2 4. F = MA --> .040 x 20 = .8 N 5. a) The bowling has a greater mass, thus meaning it has a greater inertia, so it is harder to stop and start moving.  b) Because mass and acceleration are inversely proportional, you would have to put more force on a bowling ball to achieve the same acceleration as the baseball. 9. The force of your hand is still acting upon the ball until an unbalanced force hits the ball. 10. Total force = Fa + Fb --> 50 N + 40 N = 90 N 11. Combined Force = adults x force --> 4 x 200 N = 800 N 12. A = F/M --> 125/.700 kg = 179 m/s^2 13. 130 N at 67 degrees NE 14. 6403 N at 39 degrees Work Shown for 13-14: 15. F(weight)=mg --> F=12.8 x 9.8 --> F= 125 N 16. a) 50 N at 53 degrees b) 8.9 m/s^2 17. a) 36 N at 34 degrees b) 0.36 m/s^2 c) 0.5 m/s^2 Work Shown for 16-17:   18. And here's the pitch, a swing and miss he struck him out! Wow, the pitcher is really on tonight. His velocity came out to be 100 miles per hour or 44.7 meters per second. We should remember, Chuck, he is throwing an object that has a mass of 0.145 kg, so it should go much further and get to a person faster than let's say a bowling ball. Next batter, and it is a shot that goes into the outfield with such great force of approximately 250 N. What a hit!
 * 1. **
 * a) F = ma --> 70 x 5 = 350 N **
 * b) m = f/a --> 800/10 = 80 kg **
 * c) A = f/a --> 70/7 = 10 m/s^2 **
 * d) M = F/a --> 400/5 = 80 kg **
 * e) A = f/m --> -1500/100 = -15 m/s^2 **
 * f) F = ma --> 100 x -30 = -3000 N **


 * Physics Plus **




 * What do you think now? **
 * A force is a push or pull that is measured in newtons. Force has a direct relationship with acceleration, but acceleration and mass have an inversely related relationship. If there is acceleration, then there must be a force. When you apply a force to an object with a small mass, then the acceleration can be large. If you apply a force to an object with a large mass, the acceleration can be smaller. Thus, the less the mass, the more acceleration and vice versa. If both pushed with a same force, a tennis ball will travel much farther than a bowling ball. Tennis balls have less mass than a bowling ball, so you do not need as much force to get it moving.

**﻿Chapter 2, Section 4**

 * What do you think?**
 * It is determined by the amount of strength and force you exert when launching the object. The angle you throw the object at, the weight of the object, the velocity, and how high it is thrown will also determine how far the object will go into the air before it lands.


 * Investigate**

Part A - see group wiki Part B - see group wiki

**Part 3: Use a Simulation to investigate further** a) Set the launch velocity to 5 m/s and “FIRE”. Record the time to the ground and use the measuring tape (initially located in the bottom right corner) to measure the range (horizontal distance from the starting point). b) Repeat in 10 m/s increments up to 55 m/s, recording the time and range after each trial.
 * 1) Set the angle to zero and choose baseball. Do not change these settings for any trials in this part.


 * Object || Angle (°) || Initial Speed (m/s) || Range (m) || Hang Time (s) ||
 * Baseball || 0 || 5 || 2.5 m || 0.5 s ||
 * ^  ||^   || 15  || 7.4 m || 0.5 s ||
 * ^  ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">25  || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">12.4 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0.5 s ||
 * ^  ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">35  || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">17.3 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0.5 s ||
 * ^  ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">45  || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">22.3 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0.5 s ||
 * ^  ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">55  || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">27.2 || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0.5 s ||

<span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">a) Raise the platform under the cannon to any height. <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">b) Set the angle to zero and “FIRE”. Record the time to the ground and the range. <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">c) Move the launcher to several higher and lower positions and repeat the experiment.
 * 1) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Choose Tankshell and set the initial velocity to 18 m/s and the initial angle to 0°. Do not change these settings for any trials in this part.

<span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">(m) || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Time <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">(s) ||
 * <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Object || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Angle (°) || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Initial Speed (m/s) || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Initial Height (m) || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Range
 * <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Tankshell || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0 || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">18  || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-1.2 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">8.9 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">0.5 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-5.8 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">19.5 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.1 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-6.6 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">20.9 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.2 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-7.5 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">22.3 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.2 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-9.0 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">24.4 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.4 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-10.4 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">26.3 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.5 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-11.8 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">27.9 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.6 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-13.0 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">29.4 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.6 s ||
 * ^  ||^   ||^   || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">-14.8 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">31.3 m || <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1.7 s ||

<span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">Discussion Questions
 * 1) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What happened to the time in the air as the horizontal launch velocity was increased?
 * 2) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">The time stayed the same.
 * 3) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What happened to the range as the horizontal launch velocity was increased?
 * 4) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">The range increased every time as the horizontal velocity increased.
 * 5) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What happened to the time in the air as the initial height was increased?
 * 6) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">The time increased as the initial height increased.
 * 7) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What happened to the range as the initial height was increased?
 * 8) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">The range increased as the initial height was increased.
 * 9) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What factors seem to influence the time of flight of a projectile?
 * 10) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">A decrease or increase in the initial height seemed to influence the time of flight of a projectile.
 * 11) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">What factors seem to influence the range of a projectile?
 * 12) <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">A increase or decrease in initial height and velocity (initial speed) seemed to influence the range of a projectile.


 * Physics Talk**


 * Summary:** <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">A trajectory is a fancy word for path, which we use to determine projectiles. Projectile is an object acted on only gravity. There is not a projectile if there is any air resistance. The x-component and y-component of all vectors are independent. X-components are only affected by other x-components and y-components are only affected by other y-components. Vertical velocity affects vertical distance and horizontal velocity affects horizontal distance. (X is horizontal and y is vertical). The time it takes for a horizontally launched projectile to reach the ground (hang time) is the same as the time it takes to drop. Acceleration due to gravity is -9.8 m/s^2 or -10 m/s^2. Vertical velocity changes by -10 m/s every second. Horizontal velocity does not ever change. Vy is always 0 m/s at its maximum height. Throwing horizontally results in the same path or trajectory as the second half of a ball thrown at an angle.


 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Checking Up **

<span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">1. If a pen and a ruler were dropped together from the same height, they will hit the floor at the same time. Acceleration acts upon them in the same way and there is no air resistance. <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">2. When an object falls vertically down to the ground, its velocity is not the same. It is approximately 10 m/s per second. <span style="color: #008080; font-family: Arial,Helvetica,sans-serif;">3. If a ball is thrown upward, then the ball's velocity at its highest point is 0 and the ball's acceleration is approximately -9.8 m/s^2.


 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Physics To Go **

1-2.  4. Mom - She believed that the dropped bullet would hit the ground first. Dad - He believed that the shot bullet and the dropped bullet would hit the ground at the same time. Rob - He believed that the shot bullet and the dropped bullet would hit the ground at the same time. Mike - He believed that the dropped bullet would hit the ground first. Both my mom and my brother Mike thought that because of the angle of the dropped bullet, as it is 90 degrees that the dropped bullet would fall faster. 6. After observing the ball and chair in this section, the statement is truthful because the chair moving horizontally and the ball went straight up and then back down. Vertical motion has no effect on the horizontal motion. Vertical velocity approximately changes at -10 m/s^2. On the other hand, horizontal velocity does not change. 7. If you neglect air friction, arrow A (horizontally shot) and arrow B (dropped) will land at the same time. This is all due to gravity. 8. 3.6 km/h at 33.7 degrees. 9. a) 11.98 m/s b) 23.96 m  10. a) 8.5 m/s b) 4.25 m  Work for problems: 11. And the pitcher starts his windup, leg lift, fires with a change-up at a speed of 80 mph. The hitter sees this and swings..He crushes the ball, that weighs .145 kg with great force, approximately 270N, as it goes into the outfield. The outfielder turns the opposite direction to catch up to the crushed ball and make a spectacular catch. He is still running and the baseball is accelerating at 9.8 m/s^2. The outfielder catches up to the ball and sees the ball at its highest height, with a velocity of 0 and the ball drops down right into his mitt with an acceleration of -9.8 m/s^2.

**Video Clip**

[] This video clip explains angular trajectory and how they are applied in sports. The shape and angle of a trajectory plays a part in basketball, as you can tell. They analyze Allen Iverson's jump shot to express this and mention that in order to make a point, you have to shoot the basketball at the correct angle. Basketball shots should be released at an angle of 45 to 60 degrees. This is the proper angular trajectory when shooting the basketball. In soccer, you have to have the proper angle to make a goal. They analyze David Beckham and how he realizes that in order to make a goal, you have to angle the ball perfectly.


 * Physics Plus**

Work: Answer: 49.5 m/s at -29 degrees.

**What do you think now?**
 * When determining how far an object will travel before landing, you must measure your initial height, as well as, your launch velocity. When either initial height or launch velocity is decreased or increased are some factors. The angle at which the object is going and the speed at which it is traveling also will determine how far an object will travel.

Chapter 2, Section 5

 * What do you think?**
 * The trajectories of projectiles launched from the ground are affected by the angle. If you have a larger angle, the higher it will go in the air. If you have a greater velocity and launch speed, you will have a larger range, thus changing of range. In basketball, you have to have the shoot the ball at the right angle to make it in the basket and have a right trajectory.


 * Physics Talk**


 * Summary:** This physics talk talks about the different models of projectiles and the angles that affect them. Projectiles have two motions that act at the same time and do not affect one another. The first motion is constant speed along a straight line, corresponding to the amount of launch speed and its direction. The second motion is downward acceleration at 9.8 meters per second^2. We use computers and graphing calculators to model the trajectories of projectiles. Launch angle, speed, height, and range are manipulated with these tools, in order to help us understand the motion of a projectile. All trajectories have a path that makes a parabola. Some key facts include that the 45 degree launch produces the greatest range, the distance traveled at pairs of angles such as 30/60 and 20/70 are identical. All in all, smaller angles have greater horizontal velocities, but aren't in the air that long. Larger angles have smaller horizontal velocities but are in the air a longer time.

**Checking Up**

1. The two types of motion include constant speed along a straight line and downward acceleration of 9.8 m/s^2. 2. The fundamental requirement that a scientist must meet when proposing a model of some natural phenomenon is to match reality in nature. 3. As the angle of launch is increased from 10 to 80, the distance will be the same since they are complimentary angles. The horizontal velocity of the smaller angle will be larger than the horizontal velocity of the larger angle.


 * Physics Plus**

1. d = 8.26 m ; t = 1.18 s 2. d = 49.5 m ; t = 1.10 s  Work:


 * Physics To Go**

1. 45 degrees would produce the greatest range. This is because if an object was launched at this angle, you would cover the most distance. 2. a) If the angle is more than 45, then the amount of time in air (hang time) would increase. b) If the angle is less than 45, then the amount of time in air (hang time) would decrease. 3. a) A launch angle of 60 degrees would produce the same range as a launch angle of 30 degrees. b) A launch angle of 75 degrees would produce the same range as a launch angle of 15 degrees. 4. I think that this occurs because the initial velocity of x is greater than the initial velocity of y, which means that the launch angle must be less than 45 degrees. 5. I think he was successful in both events because he must have been a fast sprinter and had a high vertical. For long jump, he must have used his abilities of speed to get a nice running start to land the jump. He must have jumped at the best angle to obtain his maximum range. 6. a) Acceleration of the ball points downward. You use the equation, A = -9.8 m/s^2. b) The direction of the ball's velocity is pointing south east. Vmax is equal to Vi x because Vy = 0 at maximum height. 7. a) 29.4 m/s b) 5.0 m/s c) 15 m Work:   8. 45 degrees would result in the ball traveling the longest horizontal distance if air resistance is neglected.  9. The biggest angular direction would produce the greatest projectile height. It would be closest to 90 degrees.  10. a) Acceleration's direction would be downwards. b) 4.5 s c) 90 m  Work:


 * What do you think now? **
 * ** 45 degree launch produces the greatest range, the distance traveled at pairs of angles such as 30/60 and 20/70 are identical. All in all, smaller angles have greater horizontal velocities, but aren't in the air that long. Larger angles have smaller horizontal velocities but are in the air a longer time. **

Chapter 2, Section 6

 * What do you see?**
 * I see a man in a chair pushing his feet against the wall. He then pushes himself off the wall, which propels himself in the opposite direction.


 * What do you think?**
 * If I were to teach someone how to jump, I would first tell them to plant their feet and get loose. Then, I would tell them to bend their knees, so that they get more distance in the air. I would then tell them to jump up as high as they can. The force from the ground will then be pushed back up to the person, giving him more distance in the air.

**Physics Talk**

**Summary:** In this physics talk, we learned all about Newton's Third Law and free-body diagrams. Newton's third law of motion tells us that for every applied force, there is an equal and opposite force. The two forces always act on different objects. One example would be the student pushing (applying a force) on the wall. The wall pushed on the student. A force diagram shows the forces acting on an object. In a free-body diagram, each force is represented by an arrow with labeled forces. A free body diagram is defined to be a diagram used to show the relative strength and the direction of all the forces acting on an object in a given situation. Inanimate objects can push back and provide force, too. For example, when you stand on the floor, your mass is pulling you down. One would fall if the floor were not applying an equal force on you. Newton's third law of motion can be described as: 1. For every force applied to object A by another object B, there is an equal and opposite force applied to object B by object A. 2. If you push or pull on something, that something pushes or pulls back on you with an equal amount of force in the opposite direction. 3. All forces come in pairs. 3rd Law: Every action has an equal but opposite reaction. It can also mean that all forces come in pairs.

1. Newton's third law of motion states for every applied force, there is an equal and opposite force present. 2. The mass is pulling the earth up on the force with an equal force of gravity. 3. A free body diagram shows us the forces acting on an object. We use arrows to interpret the direction of the force used.
 * Checking Up Questions **

**Physics To Go** 1. Yes, but the two forces are opposites. 2. There is compression present, but one cannot see it. There is no deflection but restoring forces balance downward weight. 3. When you step on the scale, you don't really measure your weight, but you measure your normal force. There is normal force from the scale and a normal force from yourself. 4. The forces are equal but opposite. the bat breaks because the force of the ball is too big for material to withstand. 5. The forces are equal but opposite. The smaller player has bigger acceleration. 6. Force of the boards on player will equal the force of player on boards 7. The cushioning of the catcher's mitt has compression, so it is able to have a deformation. This causes lower acceleration which reduces force on hand. 8. a) Oh, Wow! It is a shot to right field. The right fielder is backing up and running. He goes all the way to the warning track and slams right into the wall. He obviously did not notice that wall, but it seems fine and catches the ball. The player did hit that wall with great force but the wall came back with a force of the exact same value which made him alright. b) When one falls, there is a deflection. If one were running, then fell to the ground, the deflection of the ground would cause a force. I would obviously be enthuastic during this part of the segment to make more exciting and interesting.

**What do you think now?**
 * After reading and analyzing the section, I can teach someone, who has never jumped before, the art of jumping. When you jump, there is a two normal forces. They include: The ground acting on you and you acting on the ground. Taking this in account, you want to bend your knees and be on the balls of your feet. You need to apply force to the ground, then you jump. The force of the ground helps you propel upwards. Your force and the force of ground are equal. We push down on the floor to jump, while the floor pushes us upwards to jump.

Chapter 2, Section 7

 * What do you think?**
 * Some sports require special shoes because of friction. If you were ice skating, you need special shoes. If we were wearing sneakers, we would not be able to stop due to the ice rink being frictionless. In general, many sports play on different surfaces. Features include a blade, for ice skating and others in order to get friction between you and the ground.


 * Physics Talk**
 * Summary:** Friction is defined to be the force that resists relative motion between two bodies in contact. There was a second force on the shoe of equal strength and in the opposite direction when we pulled it. This was the force due to friction between the shoe and surface. The pulling force was equal to the frictional force, and the net force was 0. A normal force is defined to be the force acting perpendicularly or at right angles to a surface. The coefficient of sliding friction is defined to be the dimensionless quantity symbolized by using the letter, μ, as its value depends on the properties of the two surfaces in contact and is used to calculate the force of friction. The formula for, **μ** , is force of friction/perpendicular force exerted by the surface on the object (normal force). There are three key rules to the coefficient of sliding friction, including: 1. It does not have any units because it is a force divided by a force. 2. It is usually expressed in decimal form. 3. It is only valid for the pair of surfaces in contact when the value is measured; any significant change in either of the surfaces may cause the value of the coefficient to change.

**Checking Up** 1. The force of friction is equal to the force on the spring scale. This is because the pulling force was equal to the frictional force. Because they were in opposite directions, the net force is equal to 0. 2. The coefficient of friction has no units. This is because it is a force divided by a force. 3. The force of friction is equal to the force required to slide an object with constant speed.

**Physics To Go** 1. Bad weather conditions and lack of good shoes would affect a track athlete. If it is raining outside, the runner would be running on a wet surface and would need more friction between the surface and shoe. Thus, they would want a little spike to gain friction between their shoe and surface, so that they would not slip or fall. Maybe the athlete can buy shoes that are a little heavier, since it would have more friction. 2. When snowboarding, snowboarders need as little friction as possible to glide across the snow. To do this, they put wax on their snowboard, which reduces the amount of friction. 3. She cannot be sure that the same shoes will provide the same amount of friction when playing on another court. The away court may have a little rougher or smoother surface than her home court. 4. Tennis players definitely have different shoes on clay, grass and hard surfaces. When playing on a hard surface, they need more friction on their shoe. When playing on a clay or grass court, the player does not need as much friction. So, they use different shoes because all have different friction. 5. Coefficient of friction = f/N --> EFy = MAy --> N = w = 600 N --> 0.03 = f/ 600 N --> f = 18 N --> F - f = 0 --> The minimum amount of horizontal force would be 18 N. 6. **Known: m = 1000 kg --> µ = 0.55 --> Vf = 0 --> t = 6 s** **a)** w = mg  = (1000) (9.8)  w = 9800 N  **b)** EFy = ma N = w  µ = f/N ---> 0.55 = f/9800 = f = 5390 N  **c)**  EFx = ma -->  - f = ma --->  -5390 = 1000a >  -5.39 m/s^2 = Acceleration  **d)** Vf = Vi + at ---> 0 = Vi + (-5.39)(6) ---> 32.34 m/s = Vi 7. Air resistance and water resistance do have the same affects as sliding friction. They remain constant, but are the speed changes. Whenever one is running towards the wind, the wind is blowing back at them. Air and water resistance both depend on speed. 8. It does set a limit on how fast you can start in a sprint. It means that even with strong legs, you cannot have more than a certain acceleration. In order to solve this problem, you should go and buy a pair of shoes with smoother bottoms to reduce friction. 10. Friction is important when running because you need to have friction between your shoes and surface, so that you will not slip and be able to stop. Cleats are used to have more friction. Cleats have spikes on the bottom in order to keep the footing of a player on different surfaces. No friction would mean no walking. 11. Hello, folks. Welcome to Monday Night Football. Today, we are experiencing icy conditions on the football field. The players better be packing those heavy shoes with spikes to get more friction between the ground and their cleats. Today, we should see a lot of slipping and falling.

**Physics Plus**


 * What do you think now?**
 * Some sports require special shoes because of friction. If you were ice skating, you need special shoes. If we were wearing sneakers, we would not be able to stop due to the ice rink being frictionless. In general, many sports play on different surfaces. Features include a blade, for ice skating and others in order to get friction between you and the ground. Another feature would be a spike to gain more traction between the surface and your shoe. We know this from the coefficient of friction. If the coefficient of friction is high, then it is hard to slide. If the coefficient of friction is low, then it is easy to slide. The coefficient of friction is represented by µ.


 * Lab: Bowling with Blocks**

Table 1 Mu = 5/12 = .42
 * Part I**
 * Tension (N) || Tension (N) || Tension (N) || Ff (N) || Total Weight (N) || Mu || Class Average of Mu || % Difference ||
 * 5 N || 5 N || 5 N || 5 N || 12 N || .42 || .33 || 27.3 % ||
 * Sample Calculations Part I**

% difference = abs(Class Av - Your value)/class average * 100 = 27.3 %


 * Part II**

Table - Friction and Kinematics

Fy = MAy --> N - W = 0 --> N = W --> W = (.2) (9.8) --> N = 1.96 N
 * Mass (g) || Mass (kg) || Measured Time (s) || Measured Distance (m) || Ff (N) || Acceleration (m/s^2) || Calculated Vi (m/s) || Calculated time (s) || % error ||
 * 200 g || .2 kg || 1.81 s || 6.58 m || .65 N || -3.25 m/s^2 || 6.5 m/s || 2 s || 9.5 % ||
 * 200 g || .2 kg || 1.37 s || 3.23 m || .65 N || -3.25 m/s^2 || 4.6 m/s || 1.42 s || 3.5 % ||
 * 200 g || .2 kg || 1.22 s || 4.29 m || .65 N || -3.25 m/s^2 || 5.3 m/s || 1.63 s || 25 % ||
 * Sample Calculations Part II**

(Class average: Mu = .33) Mu = f/N --> .33 = f/1.96 --> f = .65 N

Fx = MAx --> 0 - .65 = .2a --> -.65 = .2a --> a = -3.25 m/s^2

Vf^2 = Vi^2 + 2ad --> 0 = Vi^2 + 2(-3.25)(6.58) --> 42.77 = Vi^2 --> Vi = 6.5 m/s (Repeat this step for other two trials)

Vf = Vi + at --> 0 = 6.5 + -3.25t --> 3.25t = 6.5 --> Calculated Time = 2 seconds (Repeat this step for other two trials)

% Error = abs(Calculated Time - Measured Time)/Calculated Time * 100

Part III: Questions/Conclusion 1. In Part I, The coefficient of friction means the amount of friction between the block and the floor. 2. My mu came out to be .42, while the class average seemed to be .33. My total percent difference was 27.3%. The results should be the same because we are all using the same block and equipment. But, if one had a random error, it could alter the results. 3. The times agreed pretty well. For my first two trials, my percent error was rather low. It was only 9.5% and 3.5%. For the last trial, I had a higher percent error of 25%. 4. The theoretical physics we are learning in class do seem to be applied in the real world. Many people do not realize how many sports display Newton's laws of physics. In this lab, we were bowling a block. So, a good example for a sport where the coefficient of friction is used would be bowling. 5. Three sources of experimental error include if the stop watch was not stopped right away, if the tape measure was not properly set (not straight), or if the block flipped when it was bowled. If the partner did not stop the stop watch in time, then our times would get altered, thus altering the calculations. If the tape measure was not straight, then the distance would be altered. If the block was flipped, the distance and time would be altered.
 * (FOR THIS LAB, I USED THE AVERAGE COEFFICIENT OF FRICTION FOR THE VALUE OF MU)**

Chapter 2, Section 8

 * What do you think?**
 * They can't vault over a 12 m high bar with a pole 11 m long because the heavier the object, the less acceleration the pole vaulter will attain.
 * Factors that limit the height a pole vaulter can attain include the length of the pole, as well as the mass, momentum and deflection.


 * Investigation**

__Prelab__: a) Record your technique for blasting the penny high in the air: You need to bend the ruler a lot for it go high. The more you bend it the higher the penny will go.   b) What factors about the ruler and how it is positioned determine the height the penny achieved? How far the ruler sticks out from the table, greater deflection, position of the penny (closer to the end), and the mass of the coin. __ Lab: __ a) What will you be able to conclude as a result of your experiment? We will be able to conclude where on the ruler the penny should be placed so it will hit the ceiling.   b) What data will you record? The position of the penny on the ruler and how high the penny goes. c) What tools will you use to make your measurements? We will use a penny, meter stick, a ruler, and tape. d) How will you analyze your data? We will make a table recording the height and the position of the penny and we will look what position the penny went the highest.

Investigation 8: Height of a pole vaulter

Variable tested: The Position of the Penny on the Ruler. Methods and Materials: Penny, ruler, meter stick, and tape. Data Table: Conclusion: The closer the penny is to the tip of the ruler, the higher it is going to fling into the air. So once we were getting closer to 1cm the penny was going higher and higher.
 * Position || Height ||
 * 15cm || 22cm ||
 * 12cm || 80cm ||
 * 9cm || 120cm ||
 * 6cm || 180cm ||
 * 3cm || 190cm ||


 * Physics Talk**


 * Summary:** This physics talk explains all the types of energy. Energy abides by the law of conservation. A force can change the speed and the position of any object, doing so, it allows the position and speed to change back to its original state. This states that energy cannot be destroyed and can be transformed from one form to another, but the total amount of energy remains constant. One type of energy is known as kinetic energy. Kinetic energy is defined to be any energy with motion. The equation used for kinetic energy or KE is 1/2mc^2. Another type of energy is gravitational potential energy. Gravitational Potential Energy is defined to be the energy an object possesses because of its vertical position on Earth. The equation for Gravitational Potential Energy or GPE is Mass x Gravity (9.8) x Height. The sum of these two energies will always be constant and the same. Another type of energy is work. Work is defined to be the product of the displacement and the force in the direction of the displacement. The equation for work or W is Force x Distance. The last type of energy is Elastic Potential Energy. This is the energy of a spring due to its compression. The equation for Elastic Potential Energy or EPE is 1/2kx^2. All types of energy are measured in Joules. A Joule is equal to 1 N x m.

1. A force is required for the energy of an object to change. 2. The penny attains its energy from the ruler due to its "spring", which is EPE. 3. The pole vaulter attains kinetic energy from his running. The KE is then transferred into Gravitational Potential Energy because he is rising over the pole. 4. Joules are the units of the energy.
 * Checking Up**

**Physics To Go**

1. When the shot put begins, there is work being done. This work is then transformed into kinetic energy from the movement of the shot put. That same kinetic energy is then changed to GPE from the height of the shot put. As the shot put comes to a stop, there is work being done. 2. The golfer goes up to the golf ball on the tee and swings, doing Work. When the ball gets lift, It has kinetic energy and gravitational potential energy. When the ball is its on its way down, there is kinetic energy. Then, ball comes to a stop and there is work being done again. **3. KE = GPE** **1/2mv^2 = MGH** **1/2(12)^2 = (9.8) h** **7.3 m = h**

4. The factor that limits the height is the initial velocity. 5. Using the Law of Conservation of Energy, I can determine that when the temperature is increasing, the height is decreasing because there is less heat, which is energy.

**6. KE = GPE** **1/2mv^2 = MGH** **1/2v^2 = (9.8) x (4.55) = 44.59** **V = 9.5 m/s**

**7. KE = GPE** **1/2mv^2 = MGH** **1/2v^2 = 9.8 x 6.14** **V = 10.97 m/s In this case, Sergei's speed was faster than Emma's.**

**8.** **a) GPE = KE**  **MGH = 1/2mv^2**  **2 x 9.8 x 100 = V^2**  **1960 = v^2**  **44.27 m/s = v**  **b) If you do not have mass in this calculation, you can still finish the equation because mass is shown on both sides of the equation, which means that they would cancel out.**

**9.** **a) W = EPE**  **W = 1/2kx^2**  **W = 1/2 x 1500 x (.25)^2**  **W = 46.88 J**  **b) EPE = KE** **46.88 = 1/2mv^2** **= 1/2 (.1) (v)^2** **v = 30.6 m/s**

**10.** **a) EPE = W**  **1/2kx^2 = F x d**  **1/2 x (315) x (.3)^2=W**  **W = 14.2J**  **b)** **W = Force x Distance** **14.2 = F(.3)** **F = 47.3 N**

**11. GPE=EPE** **MGH = 1/2kx^2** **(.04) x (9.8) x (1) = 1/2 x (18) x (x)^2** **x = .21m**

12. a) Force = Mass x Acceleration. This equates to N=kg x m/s^2. b) GPE = Mass x Gravity x Height. This equates to (kg) x (m/s^2) x (m) N x m= J. c) KE = 1/2mv^2. This equates to 1/2(kg)(m/s)^2 ; which equates to 1kg x 1 m/s^2 = J; kgm/s^2 x m=N x m.  d) EPE = 1/2kx^2. This equates to 1/2 (Nm) x (m)^2. In the end, it equates to N x m. 13. It starts out with EPE, which further leads into KE which then leads into GPE. Finally, there is kinetic energy with work being done at the end when they hit the water to a stop. 14. In order to get the ball into the air, there must be work being done. This same work will transform into kinetic energy, and then to gravitational energy because it goes into the air. 15. The ball needs the energy of work to get moving. The work is transformed into kinetic energy, moving and increasing speed while in the air. The kinetic energy is transformed into gravitational energy, then back to kinetic, as the ball is coming back down. In the end, work is done, bringing it to a stop. 16. A pitcher starts his wind up and throws a fastball that has a velocity of 95 mph. The batter is transferring work to swing the bat and hit the ball with as much power as possible. As the ball is increasing speed while in the air, the same work from the batter has transformed into kinetic energy. The outfielder starts to book it and run hard to track down the ball, while the ball is transfered from kinetic to gravitational potential energy because it is at a higher point then before. The outfielder reaches the warning track and the ball is gone. A homer. The ball rolls behind the fence and then finally comes to stop, using work.

**What do you think now?**
 * Even though champion pole vaulters can clear a 6.0-m high bar with a 5.5-m long pole. They can't vault over a 12.0-m high bar with a pole 11.0-m long because speed is the only factor that matters. You cannot double your height and double your pole and believe that you can clear the bar. It is affected by the speed at which you travel.

Chapter 2, Section 9

 * What do you think?**
 * The hang time of some athletes do not defy the pull of gravity. The hang time is however high the athlete goes. They do not stay in one particular spot for a while.
 * A world class figure skaters don't defy gravity to remain in the air long enough to successfully complete a triple axel. They do not stay in one spot for a while.


 * Investigate**

**Pre-Lab** 2. The skater is in the air for 20 frames. 3. The amount of time in the air = 2/3 of a second 4. The skater did not defy gravity. It looks like he is defying gravity, but in reality, his change in placement is really small, which we cannot see. 5. The basketball player was in the air for 31 frames. He stayed in the air for about 1 second. He did not defy gravity at any point either.

**Instructions** **PICTURE OF CALCULATED FORCE: ** 1. First, you have to bend your knees. From here, you push off the floor. Then, you unbend knees and you go airborne for some height off the floor. The force being exerted is gravity. We are initially doing work from unbending the legs and we end up with gravitational potential energy (GPE). W = GPE 2. We would need to know your weight in order to measure the force needed to jump to a certain height. a) We will be able to conclude the amount of force exerted when jumping vertically. b) We will record the measurements of our height of jump and weight. c) We will use a scale in newtons to measure weight and a meter stick to measure the height. d) We will construct a data table that will display the measurements of both height and weight. We will also display a graph of our jump. 4. Calculations: Mass = 73 kg Distance = .2 meters Height = .42 meters W = GPE --> Fd = mgh F (.2) = 73 (9.8) (.42) F = 1502.34 N 5. My measured force was accurate to the calculated force. My measured force was 1502.34 N and my calculated force was 1517.51 N. I was not too far off between both calculations.

Percent Error = abs(Calc. Value - Exp. Value) / Calculated x 100 -- My percent error was around 10 percent.

**Physics Talk**

**Summary:** ﻿When a person is in the ready position, you have elastic potential energy. As you move toward the launch position, you exchanged the EPE for an increase in GPE and KE. As you rise in the air, you lose the KE and gain even more GPE. Here is a table to show: The energy of these three positions are equal. The greater the vertical height equates to a greater gravitational potential energy. When someone is jumping on a trampoline, the potential energy from the height you are jumping would provide KE when you landed on the trampoline. When you are descending, your KE would continue because you would be losing GPE when doing this action. The trampoline gains EPE by stretching. The Conservation of Energy is defined to be the total of all energies at any time will equal the other total of energies.

1. EPE happens when bending the knees, and being in the process of launching upwards. The knees are acting as spring when bending them. 2. In the launch position, the student would have kinetic and gravitational potential energy. At the peak position, there would be a high GPE. 3. Three types of energy include light energy, sound energy, and chemical energy.
 * Checking Up**


 * Physics To Go**

**1. W = GPE** **W = MGH** **W = (50) x (9.8) x (1)** **W = 490 J**

2. In the beginning, there is work starts and there is GPE, which turns into kinetic energy, and work starts when it breaks. 3. To determine this, we would use slow motion like what we did on the Prelab. We now know that there is no such thing as hang time and the displacement is always changing. 4. Any person making this statement should definitely have evidence to prove it. Whenever doing an experiment, you have prove the facts and never can give false evidence. 5. To increase one's maximum height, one would have to increase their muscle strength by increasing force or their mass decreasing, but not strength.

**6. Work = Force x Distance** **a) 1 x** **1= 1 J** **b) 1 x 10=10 J** **c) 10 x 1=10 J** **d) .1 x 100= 10 J** **e) 100 x .1= 10 J**

7. The same answers as number 6, due to the fact of the law of conservation of energy. 8. These answers are the same as above too because of the law of conservation of energy.

**9. W = Force x Distance** **W = (50) x (43)** **W = 2,150 J**

**10. KE = 1/2mv^2** **KE = 1/2 x (62) x (8.2)^2** **KE = 2,084.4 J**

**11. a) F = Mass x Acceleration** **30 = (5) x (a)**  **A = 6m/s^2**  **b) W = Force x Distance** **W = (30) x (18.75)** **W = 562.5 J**

**12. a) W = Force x Distance** **40,000 = 3200 x (d)**  **d = 12.5 m**  **b) 2.7 m/s^2**

**13. W = KE** **W = 1/2mv^2** **W = 1/2 (.150) (40)^2** **120 J**

**14. W = KE** **Fd = 1/2mv^2** **(417) d = 1/2 (64) (15)^2** **17 meters**

15. **It would be 1000 Joules of work out.**
 * || KE || GPE || EPE || Sum ||
 * running || 1000 J || 0 || 0 || 1000 J ||
 * full bend of pole || 100 || 0 || 900 || 1000 J ||
 * peak height || 0 || 1000 || 0 || 1000 J ||
 * Landing || 850 || 150 || 0 || 1000 J ||
 * Cushion Collapse || 0 || 0 || 0 || 0 ||

16.
 * || KE || GPE || EPE || Sum ||
 * Peak Height || 0 || 1000 || 0 || 1000 J ||
 * Landing || 900 || 100 || 0 || 1000 J ||
 * Lowest Height || 0 || 0 || 1000 || 1000 J ||

17. 18. And we are here at the summer olympics with the long jump. The runner starts his stride..runs...oh and what a jump by him. He really was in the air for a while. But, we should recognize that he was not defying gravity. He was moving in different positions each frame and never stayed in one particular spot.
 * || KE || GPE || EPE || Sum ||
 * Top of Mountain || 0 || 1000 || 0 || 1000 J ||
 * Middle || 700 || 300 || 0 || 1000 J ||
 * Bottom || 1000 || 0 || 0 || 1000 J ||

** Physics Plus **

**1. a) GPE = KE** **MGH = 1/2mv^2**  **(9.8) x (20) = 1/2v^2**  **392 = v^2**  **19.8 m/s = v**  b) The mass of the cart does not matter due to the fact that there is mass on both sides of the equation. Thus, they will cancel out.

**2. KE = EPE + GPE** **1/2mv^2 = 1/2kx^2 + MGH** **1/2 (.300) v^2 = 1/2 (60) (.40) ^2 + (.300) (9.8) (2)** **v = 4.2 m/s**

**3.** **GPE=KE** **(200) (9.8) h= 1/2 (200)** **h=20 m**

**What do you think now?**
 * After analyzing this section, I can further elaborate on my answer. A world class figure skater definitely cannot defy gravity. There are always moving, yet we cannot see it because the displacement is very small. When we see an athlete get lift-off and hang-time, they are not defying gravity. Again, they are moving a subtle amount every frame. This pertains to all athletes, from the slam dunk to the triple axel, not one athlete can defy gravity.