Chapter+Two

toc =**Amanda Steiger's ActivePhysics Wikilog**= =**Chapter 2**=

Section One
Prompt: Find one reference to the science of any sport in current events. Use the sports section of a local paper, a sports magazine, or online sports journal. Summarize the article, quote the section referencing the physics, and be sure to cite your source! Put it all in your wikilog. I chose to use the NY Times article //Up in the Air, and Down, With a Twist// (http://www.nytimes.com/2010/02/02/science/02ski.html). The article, originally published in February of 2010, discusses the science behind sports like skiing and figure skating, concentrating mainly on freestyle aerialists. Much of the text explains the forces and physics at work in these competitive sports. "These athletes... are not actually throwing caution, along with themselves, to the winds. It is not fate that plops them down at the end of their jumps, more or less upright and safe, in a cloud of powdery snow. It is physics, and plenty of preparation," the article tells readers. '"Once [an aerialist is] in the air, the only force on him is gravity,' Dr. Johnston [a physics professor at Weber State University in Ogden, Utah] said. 'You could trace his center of mass as a perfect parabola through the whole thing. From the physics point of view, that’s one of the beautiful things.'" The article is interesting, very instructional, and shows how important physics is in relation to sports.
 * Homework 11/3/10**

Prompt: Every sport includes moving objects or people or both. That is what makes sports entertaining. How do figure skaters keep moving across the ice at high speeds for long times while seeming to expend no effort? Why does a soccer ball continue to roll across the field after it has been kicked? Response: Physics plays a huge role in sports. A figure skater or a soccer ball would continue to move because of inertia. Once an object is in motion, it will stay in motion until an unbalanced force acts upon it. By the same principle, an object at rest will stay at rest until an unbalanced force acts upon it.
 * What do you think?**

Hypothesis: The vertical height that the ball reaches on the opposite side of the track is equal to the vertical height from which the ball is released. __//First Trial//__ Initial Height: 6.80m Maximum Height on Opposite Side: 6.80m __//Second Trial//__ Prediction: I predict the ball will be able to achieve a larger maximum height, because the length of the opposite side has been increased. Outcome: The ball's maximum height during this trial was 6.61. My prediction was incorrect. The slope of the opposite side had been decreased, which prohibited a larger maximum height. Description: The momentum of the ball is a parabola ("U") shape. __//Third Trial//__ Prediction: I predict the ball's maximum height will further decrease because the slope has further decreased. Outcome: My prediction was right. As the slope decreases, the maximum height of the ball decreased. The ball's maximum height during this trial was 6.54 5. Imagine what would happen if you changed the right-hand section of the track so that it would be horizontal (zero slope): a. The ball's starting height would not be accessible, and he would not be able to reach it. b. The ball would continue to travel until an unbalanced force, such as friction, interfered. c. The ball would continue rolling on the horizontal track as a result of inertia. d. My prediction was correct. The ball continued to roll off the track instead of returning to his starting height. 6a. As the slope decreases, the length of the opposite track increases. 6b. As the slope decreases, the final vertical position on the opposite track decreases. 6c. To draw a conclusion, I would need to be provided with more data, such as the slope of the track. 6d. If the opposite track was infinitely long and friction-less, the ball would continue to roll forever.
 * Investigate**

Galileo, an Italian physicist, formed the Law of Inertia. Inertia is the natural tendency of an object to remain at rest or to remain moving with constant speed in a straight line. Inertia is measured in kilograms (mass). His revelation changed the way in which people viewed motion. People began to recognize that moving objects might continue to move forever unless a force, a push or a pull, stopped them. This was difficult for people to understand because it meant that objects never stop "on their own," but stop because there is a frictional force at work. Isaac Newton used Galileo's Law of Inertia to develop his own law of motion, which stated that in the absence of an unbalanced force, an object at rest remains at rest, and an object in motion remains in motion with constant speed in a straight line path. Newton also theorized that an object's mass (amount of matter) is a measure of its tendency to resist a change in motion. The greater the mass of an object, the greater the inertia of said object. Newton published the book //Principa//, which summarized his discoveries and explained his first law of motion. By applying a "running start" to an object, more momentum is achieved. Running starts increase distance and/or speed to give an advantage. Frames of reference add or subtract velocity to get relative values, and ensure an object's speed is described as "relative to" another object.
 * Physics Talk: Newton's First Law of Motion**

1. Inertia is a property of matter that resists changes in motion. 2. Newton's first Law of Motion stated that in the absence of an unbalanced force, an object at rest remains at rest, and an object in motion remains in motion with constant speed in a straight line path. 3. An unbalanced force must act on an object to stop it from moving at a constant speed. 4. A rolling ball would be naturally stopped by friction and gravity in most situations. 5. Given two differently sized masses moving at the same speed, the greater mass will have the greater inertia. 6. When describing speed, one should always be aware that it is a relative measurement. The measurement must specify the point of view.
 * Checking Up Questions**

1. If one was to push a ball to start it rolling on a friction-less surface, the ball would continue to roll forever until interrupted by some unbalanced force. 2. The ball will reach the initial vertical height, 20 cm, on the opposite ramp. 3. There is no such thing as an infinite, friction-less surface on Earth, and the experiment would have to take place in space to be successful. 4. When a hockey player hits a puck, it is giving the puck momentum. The puck will continue to move in a straight-line path until it is interrupted by another force or hits another object and changes direction. 5. The person who is standing by will see the ball traveling at 7m/s (2.5m/s + 4.5m/s) 6. The javelin's speed relative to the ground is 14.2 m/s (10.3m/s + 4.2 m/s) 7a. The cart's velocity relative to the ground when pushed towards the front of the car is 8m/s (2.4m/s + 5.6 m/s) 7b. The cart's velocity relative to the ground when pushed towards the back of the car is is 3.2m/s (5.6m/s - 2.4m/s) 7c. x=6.1m/s^2 8. The arrow left the bow at 67m/s (85m/s- 18m/s) 9a. 15/sin(45)= 21.2 cm 9b. 15/sin(20)= 43.9 cm 9c. 15/sin(15)= 57.9 cm 9d. 15/sin(5)= 172 cm 10. Three examples of Newton's First Law of Motion in sports are gymnastics, hockey, and tennis. In gymnastics, competitors take running starts before hurling themselves through the air. During a hockey game, the puck glides across the ice, as it has minimal friction. A tennis ball remains in the air as a result of the force behind the racket.
 * Physics To Go**

Prompt: At the beginning of this section, you were asked the following: How do figure skaters keep moving across the ice at high speeds for long times while seeming to expend no effort? Why does a soccer ball continue to roll across the field after it has been kicked? The ice skater effortlessly gliding across the ice at high speed and the soccer ball moving across the field are like the ball rolling along the horizontal portion of your track. What determines their horizontal speed and why do they keep moving without someone doing anything to keep them moving? Response: Horizontal speed is determined by the force that instigates movement. The ice skater or soccer ball continues to move because of inertia until friction or another opposing force halts the motion.
 * What do you think now?**

1. Within the game of curling, Newton's First Law of Motion presents itself when the "stone" or puck crashes into another object and continues to move. Friction plays a huge role in this sport- the amount of friction will affect the length the stone travels. ([]) 2. Players do not want to travel past 1st base, so the additional speed is not required.
 * Inquiring Further**

**Section Two**
Prompt: In your own words, explain the meaning of 100mi/h and 45m/s. Response: The different measurements provide different scales of distance.
 * What do you think?**

Acceleration is the change in the velocity of an object over time. Average acceleration is found by dividing the change in velocity over time elapsed. Instantaneous speed is the speed measured during an instant. Average velocity describes how fast position changes, and is usually found for large distances or times over which there may be variations. Average velocity is found by dividing total distance by total time. When V and A have the same signs, velocity is increasing. When V and A have opposite signs, velocity is decreasing.
 * Physics Talk: Measuring Motion**

1a. Evenly spaced 1b. Begins closely spaced before the distances between dots increases 1c. Begins widely spaced before the distances between dots decreases 2. 400/50= 8m/s 3. Average speed describes the standard speed over a long distance or time. Instantaneous speed describes the speed at one particular moment. 4. 100/.0028= 3600km/h^2
 * Checking Up Questions**

1. Average speed is the mean of a total trip. Instantaneous speed is the speed at one particular moment during a trip. 2a. 1000m/15s= 67m/s 2b. 84m/6s= 14m/s 2c. 9.6km/2h= 4.8km/h 2d. 400km/4.5h= 89km/h 3a. Negative acceleration 3b. Positive acceleration 3c. Constant speed 3d. Negative acceleration 3e. Constant speed 3f. Constant speed 4a. Graphs A & D 4b. Graph B 4c. Graph A 4d. Graph C 4e. Increasing acceleration, constant speed (no acceleration), increasing/decreasing acceleration, increasing acceleration 6a. a= 0.12.5/9= -1.39m/s2 6b. Negative value (velocity is positive and acceleration is negative) 7a. Constant velocity 7b. Accelerating forward 7c. Accelerating then decelerating 7d. Decelerating then accelerating 8. 100mi/2h= 50mi/h 9. No, average speed and instantaneous speed are not the same. Average speed describes the mean velocity of an entire trip, while instantaneous speed tells the velocity at a certain moment during the trip. 10. X--- X--- X -X- X--- X--- X 11. Assuming the car started from rest, the final velocity is 20m/s (4m/s x 5s) 14a. Marathon runner 14b. Indy 500 car race 14c. Swimming 14d. Drag racing 14e.Curling
 * Physics To Go**

**Physics Plus: Large Accelerations at Slow Velocity** Rebounding: bouncing off a surface and changing direction *assume acceleration is constant during entire process. 1. 100m/s^2 2. 5m/s^2 3a. 5m/s^2 3b. 5m/s^2 3c. 5m/s^2
 * velocity || acceleration || examples ||
 * small || small || golf cart, jogger ||
 * small || big || rebounding objects ||
 * big || small || large truck ||
 * big || big || airplane ||

Prompt: In your own words, explain the meaning of 100mi/h and 45m/s. 100mi/h means that the object will travel 100 miles within one hour. 45m/s means that the object will travel 45 meters in one second. By conversion, 100 kilometers per hour is equal to 27.7 meters per second, making this velocity slower than 45m/s.
 * What do you think now?**

Section Three
Prompt: What is a force? How will the same amount of force affect a tennis ball and a bowling ball differently? Response: A force is a push or a pull. The same amount of force would have a different effect on a tennis ball or a bowling ball because they have different masses.
 * What do you think?**

**Physics Talk: Newton's Second Law of Motion** Newton's second law of motion states that the acceleration of an object is directly proportional to the unbalanced force acting on it and inversely proportional to the object's mass. The direction of the acceleration is the same as the direction of the unbalanced force. When more than one force is being applied to an object, the forces must be added together while keeping in mind their respective directions. If the forces are perpendicular to each other, the Pythagorean theorem is used to find Fnet. If there are more than two forces, reduce the “horizontal” (east, west) forces and the “vertical” (north, south) forces to create two new forces, and then use the Pythagorean theorem.Weight is defined as the vertical, downward force exerted on a mass as a result of gravity A free-body diagram is a diagram showing the forces acting on an object. Free-body diagrams are used to show the relative size and direction of all forces acting on an object. To convert pounds to kilograms, divide weight in pounds by 2.2. To find a weight in newtons, multiply the mass of the object by 9.8. Weight is dependent on location, while mass is independent of location.

1. Newton’s second law of motion states that whenever an object is acted upon by a net force, it creates an acceleration on that object in the same direction as the net force, according to the formula F=ma (directly proportional to force and inversely proportional to mass). 2. If the force is constant and mass is increased, acceleration will decrease. 3. Weight is equal to an object’s mass multiplied by gravity. The force pulling on the object described is 30 N downwards. 4. Weight would increase and mass would remain the same.
 * Checking Up Questions**

**Investigation** (see Group 1 page) http://activephysics-pvrhsd.wikispaces.com/Group1.2-8-EB

**Physics To Go** before jumping || 400 N || 80 kg || 5m/s^2 || while stopping || -1500 N || 100 kg || -15m/s^2 || 3. 42N/0.30kg= 140m/s^2 4. 20.0m/s^2(0.040kg)= 0.8 N 5a. The larger the mass of an object, the greater its inertia. 5b. The larger the mass of an object, the more force is needed to accelerate the object. 9.The force of your hand would stop acting on the ball when either the ball is intercepted by another force or falls to the ground as a result of gravity. 10. The net force acting on the desk is 90 N (40N + 50N) 11. The net force acting on the car is 800 N (200N x 4) 12. The acceleration of the ball is 179m/s^2 (125N/0.07kg) 13. The resulting force is equal to 130N at 67 degrees North of East. Magnitude: 50N^2 + 120N^2= Fnet^2 Direction: tan^-1(120/50) 14. The resulting force is equal to 6403N at 51 degrees Magnitude: 4000N^2 + 5000N^2= Fnet^2 Direction: tan^-1 (5000/4000) 15. The acceleration on the object is 125 N (9.8m/s^2 x 12.8kg) 16a. The net force on the object is 50N (30N^2 + 40N^2= Fnet^2) 16b. If the object was a 5.6 kg wagon, it would have an acceleration of 8.93m/s^2 (50=5.6*a) 17a. The net force on the box is 36N (30N^2 + 20N^2= Fnet^2) 17b. The acceleration of the box is .36m/s^2 (36N=100*a) 17c. The box would accelerate at .5m/s^2 (50N/100kg=a)
 * Newton's Second Law: || F = || m || x a ||
 * Sprinter beginning 100m dash || 350 N || 70 kg || 5m/s^2 ||
 * Long jumper in flight || 800 N || 80 kg || 10m/s^2 ||
 * Shot-put ball in flight || 70 N || 7 kg || 10m/s^2 ||
 * Ski jumper going downhill
 * Hockey player "shaving ice"
 * Running back being tackled || -3000 N || 100 kg || -30m/s^2 ||

1a. Direct relationship 1b. Indirect relationship 2. Yes, there needs to be a linear (direct) relationship between the force and the acceleration. (As force increases, acceleration increases) 3. The slope of the trendline represents the mass of the objects (M+m) 4. Yes, there needs to be a indirect relationship between mass and acceleration. (As mass increases, acceleration decreases) 5. The slope of the trendline represents the force. 6. If the force acting on an object increased 6 times, the acceleration would increase 6 times. If the force was 1/10, the acceleration would also be 1/10. 7. If the mass was increased 9 times, the acceleration would be 1/9th of the original acceleration. If the mass was 1/9th as great, the acceleration would increase 9 times. 8. With friction, the acceleration would be smaller and more force would be needed.
 * Virtual Lab: Newton's Second Law of Motion**

Magnitude: size or amount of something Scalar: quantities that do not have any specific direction associated with them (magnitude only), ex. temperature, prices, time Vector: quantity that has both magnitude and direction, ex. velocity, force, acceleration Resultant: Result of two or more vectors When two vectors are collinear, how is the resultant found? The sum of the forces is the resultant. When two vectors are at right angles, how is the resultant found? The resultant is found by using the Pythagorean theorem. 1. The resultant (Fnet) is 176 N at 45 degrees North of West Magnitude: 125^2 + 125^2= Fnet^2 Direction: tan^-1(125/125) 2a. The resultant force exerted by players A and B on the hockey puck is 30N (70N- 40N) 2b. The resultant force exerted by all three players on the hockey puck is 50N (30^2 + 40^2 = Fnet^2) 2c. The direction of the net force on the puck is 37 degrees South of West
 * Physics Plus: Adding Vectors**

Prompt: What is a force? How will the same amount of force affect a tennis ball and a bowling ball differently? Response: A force is a push or a pull. The same amount of force would have a different effect on a tennis ball or a bowling ball because they have different masses. The larger the mass of an object, the more force is needed to bring the object to acceleration.
 * What do you think now?**

Section Four
Prompt: What determines how far an object thrown into the air travels before landing? Response: The force behind the object and any forces interrupting the objects path, as well as the objects mass, determines how far an object will travel through the air before landing.
 * What do you think? **

1. The coins hit the ground at the same time. 2. The coins hit the ground at the same time. 3a. The speed of the projected coin did not affect whether the two coins hit the floor at the same time. 3b.Yes, it traveled further horizontally. 3c. See notebook 4a. Increasing height increases how far the projected coin travels horizontally. Changing height does not affect the time at which both coins hit the floor. 5. I predict that the ball will end up back in the person's hand as shown in the illustration. 6. The ball traveled in an arc and ended back in the person's hand. The ball followed the person who threw it because the person continued to move at constant speed. (degrees) || Initial Speed (m/s) || Range (m) || Hang Time (s) ||
 * Investigate**
 * Object || Angle
 * Baseball || 0 || 5 || 2.5 || 0.5 ||
 * Baseball || 0 || 15 || 7.4 || 0.5 ||
 * Baseball || 0 || 25 || 12.4 || 0.5 ||
 * Baseball || 0 || 35 || 17.3 || 0.5 ||
 * Baseball || 0 || 45 || 22.3 || 0.5 ||
 * Baseball || 0 || 55 || 27.2 || 0.5 ||

(degrees) || Initial Speed (m/s) || Initial Height (m) || Range (m) || Time (s) || 1. The time in the air as the horizontal launch velocity was increased remained the same throughout the trials. 2. The range increased as the horizontal launch velocity increased. (Direct relationship) 3. The time in the air increased as the initial height increased. (Direct relationship) 4. The range increased as the initial height increased. (Direct relationship) 5. Initial height influences the time of flight for a projectile. 6. Initial height influences the range of a projectile.
 * Object || Angle
 * Tankshell || 0 || 18 || 3.6 || 66.1 || 1.2 ||
 * Tankshell || 0 || 18 || 4.5 || 71.4 || 1.3 ||
 * Tankshell || 0 || 18 || 5.8 || 78.2 || 1.4 ||
 * Tankshell || 0 || 18 || 7.4 || 85.8 || 1.6 ||
 * Tankshell || 0 || 18 || 10.5 || 98.6 || 1.8 ||
 * Tankshell || 0 || 18 || 13.2 || 108.4 || 2.0 ||
 * Tankshell || 0 || 18 || 15.5 || 115.9 || 2.1 ||
 * Tankshell || 0 || 18 || 17.4 || 121.5 || 2.2 ||
 * Tankshell || 0 || 18 || 18.7 || 125.5 || 2.3 ||

Any hit or thrown ball travels horizontally and vertically. The horizontal velocity remains the same if there is no air resistance. The vertical velocity, however, is constantly changing. As it rises, the ball slows down. As it falls, the ball speeds up. The change in velocity is always 9.8m/s every second (9.8m/s2). A projectile is an object traveling through the air or another medium.
 * Physics Talk: Projectiles and Trajectories**

1. Yes. Two objects dropped from the same height will reach the ground at the same time. 2. When an object falls vertically, its velocity is always changing. 3. If a ball is thrown upward, its velocity at the point of highest rise is 0. The ball's acceleration
 * Checking Up Questions**

1. See notebook for sketch 2. See notebook for sketch 4. Most people have a hard time believing that a bullet that is dropped and a bullet that is shot horizontally will reach the ground at the same time because it is hard for people to imagine a situation neglecting air resistance. The bullets have the same vertical velocity. 6. A projectile's horizontal motion has no effect on its vertical motion, and vice versa. This was demonstrated by Part B of the Section Four Investigate, when the ball's path was not altered though the horizontal motion was changed. 7. The arrows will hit the ground at the same time. 8. The swimmer is traveling is 3.6km/h at 56.31 degrees relative to the shore. Magnitude: V^2= 13 --> 3.6km/h Direction: tan^-1(3/2) 9a. The horizontal velocity is 11.9m/s [Vx=V*cos(37)] 9b. The football has traveled 23.9m (range=Vx*t) 10a. The horizontal velocity is 8.48 [Vx=V*cos(37)] 10b. The football has traveled 4.24m (range=Vx*t) 11. After the ball is pitched, it is horizontally launched towards the batter. As soon as it leaves the pitcher's hand, it will begin to fall at the same rate as gravity. When the player's bat makes contact with the ball, the ball receives a velocity that is at an angle with the horizontal ground. The ball will proceed to make a parabolic motion until it is intercepted or reaches the ground. Before the ball can reach the ground, it will achieve its maximum height, at which point the vertical velocity is 0 and the horizontal velocity is the same as the initial horizontal velocity.
 * Physics To Go**

2a. 43.30 [50*cos(30)] is the horizontal velocity. 25 [50*sin(30)] is the vertical velocity 2b. When time is equal to 1 second, velocity is equal to 15.2m/s 2c. When time is equal to 5, velocity is equal to -24m/s
 * Physics Plus: Vector Components**

Prompt: What determines how far an object thrown into the air travels before landing? Response: The initial velocity, height, and angle at which an object is launched determine how far it will travel before landing.
 * What do you think now?**

Section Five
Prompt: Describe the trajectories of projectiles launched from the ground at various angles. Describe how a greater launch speed of a projectile might change the range when the launch angle is the same. Response: The faster an object is launched, the greater its range will be.
 * What do you think?**

The greater the initial velocity of a projectile, the greater its range. If several objects are launched from different angles with the same initial velocity, and the theta is between 0 and 540 degrees, the range will increase as the the angle increases. If the same is true but the theta is between 45 and 90 degrees, the range will decrease as the angle increases, down to 0 degrees. 45 degrees is the maximum range. Complementary angles have the same range. Time to reach maximum height is equal to 1/2 "hang time" or total time in air. Maximum height is calculated by the kinetic equation for division using the time to reach maximum height rather that the total air time.
 * Physics Talk: Modeling Projectile Motion**

1. Two types of motion that help one understand the trajectory of a projectile are constant speed along a straight line and downward acceleration caused by Earth's gravity. 2. For a scientific model to be accepted, the model must match reality in nature. 3. The maximum range is accomplished by a 45 degree angle, with all larger angles decreasing in range.
 * Checking Up**

Part A Run 1: 9.61 Run 2: 9.60 Run 3: 9.79 Run 4: 9.55 Run 5: 9.66 Run 6: 9.80 Run 7: 9.71 Average experimental value for g= 9.67m/s squared Theoretical value for g= 9.81m/s squared % error= 1.4 percent
 * Investigate**

Part B
 * Time (s) || Velocity (m/s) || Displacement (m) ||
 * 0 || 0 || 0 ||
 * 0.1 || 1 || 0.05 ||
 * 0.2 || 2 || 0.20 ||
 * 0.4 || 3 || 0.45 ||
 * 0.4 || 4 || 0.80 ||
 * 0.5 || 5 || 1.25 ||
 * 0.6 || 6 || 1.80 ||

Part C Distance between pins: 42cm Horizontal speed for a 0.1s interval: 4.2m/s

The identical sets of mass form a parabola. The two sets of hanging mass are symmetric.

Distances remain the same from the straight line path.

1. 45 degrees 2. more.. less 3. 60 degrees, 75 degrees 4. Vi > Viy theta is less/equal to than 45 degrees 7a. 29.4 m/s 7b. 5 m/s 7c. 15 m 8. closest to 45 degrees 9. the biggest angle will the the one closest to ninety 10a. down 10b. 4.5s 10c. 90m
 * Physics To Go**

Prompt: Describe the trajectories of projectiles launched from the ground at various angles. Describe how a greater launch speed of a projectile might change the range when the launch angle is the same. Response:
 * What do you think now?**

Section Six
Prompt: Pretend that you have just met somebody who has never jumped before. What instructions could you provide to get the person to jump up (that is, which way do you apply the force when you push with your feet)? Response:
 * What do you think?**

All forces exist in pairs. The force of of object A on object B is equal in strength and opposite in direction to the force of object B on object A. For every applied force, there is an equal and opposite force. The two forces always act on different objects. This means that inanimate objects exert a force even though they are not moving, and can, in fact, "push" back. A free body diagram is a diagram showing the forces acting on an object. A center of mass is the point at which all the mass of an object is considered to be concentrated. If you push or pull on something, that something pushes or pulls back on you with an equal amount of force in the opposite direct. This is an inescapable fact- it happens every time.
 * Physics Talk: Newton's Third Law of Motion**

1. All forces exist in pairs. The force of of object A on object B is equal in strength and opposite in direction to the force of object B on object A. 2. Earth pulls down a mass with a force of gravity. The equal and opposite force in this situation would be the force the mass is exerting on Earth. 3. A free body diagram shows the different forces acting on an object in an easy, simple to understand manner.
 * Checking Up Questions**

1. Yes, the forces would be opposite and equal. 2. No. Opposing forces balance downward weight. 3. A scale has a spring with a needle attached, calibrated. 4. The force exerted by the bat and the force exerted by the ball are opposite and equal. Bats tend to break because the force of the ball is too large for the material of the bat to withstand. 5. The forces are opposite and equal. The smaller player would have a larger acceleration. 6. The force of the boards on the player are equal, but opposite to, the force of the player on the boards. 7. The padding causes lower acceleration which reduces the force on a person's hand.
 * Physics To Go**

**Section Seven**
Prompt: Why do some sports require special shoes? Why would different features of a shoe be useful for different sports? Response: Certain sports require different forms of footwear in order to provide more or less traction.
 * What do you think?**

Section seven's physics talk discusses friction. Friction is defined as a force that resists relative motion between two bodies in contact. This means that friction is always working "against" motion. Normal, meaning perpendicular, lends itself to the terms normal friction. Normal friction is defined as a force acting perpendicularly or at right angles to a surface. Free body diagrams help to organize and visualize the many forces that can be acting on an object at once and their directions. The coefficient of friction (meu) is a dimensionless quantity. Its value depends on the properties of the two surfaces in contact and is used to calculate the force of friction. The coefficient of friction is found by dividing the force of friction (f) by the normal force exerted on the object (Fn). The force of friction is equal to the force required to slide the object on the surface with a constant speed. Meu has no units, as it divides force by force.
 * Physics Talk: Friction**

1. They are equal because the force reading on the spring-scale is a result of the shoe sliding across a frictional surface. 2. The coefficient of friction has no units because it is determined by dividing a force by a force. 3. The coefficient of friction is calculated using the expression Meu=f/Fn, meaning that the coefficient of friction is equal to the force of friction divided by the normal force acting on the object.
 * Checking Up Questions**


 * Physics Plus**


 * Lab: Bowling with Blocks**

Prompt: Response:
 * What do you think now?**

Section Eight
Prompt: If champion pole vaulters can clear a 6.0-m high bar with a 5.5-m long pole, why can't they vault over a 12.0-m high bar with a pole 11.0 m long? What factors (variables) do you think limit the height a pole vaulter has been able to attain? Response: I think that the angle of the pole and the initial velocity of the vaulter influence the height attained by the vaulter.
 * What do you think?**

Pre-lab activity: a.) By placing the penny on a notch of the ruler, it is secured on the ruler and will not slip off, and can be properly launched into the air. b.) Deflection of ruler (force, elasticity), length of ruler, placement of penny, mass of object
 * Investigate Section Eight**

1a. The more force used, the higher the penny will travel. 1b. We will measure deflection and the resulting height of the penny's trajectory. We will keep the other variables constant. 1c. We will use the ruler, the penny, and another ruler. 1d. We will make a data table to analyze the data.

Trials:
 * Deflection (cm) || Resulting Height (cm) ||
 * 1 || 48 ||
 * 2 || 71 ||
 * 3 || 87 ||
 * 4 || 113 ||

This section's Physics Talk discusses the Law of Conservation of Energy. This law states that energy cannot be created or destroyed. It can be transferred from one form to another, but the total amount of energy remains constant. Kinetic energy describes energy associated with motion, while gravitational potential energy refers to energy associated with position. Gravitational potential energy is defined as the energy an object possesses because of its vertical position from Earth. When forces act on objects, energy changes from one form to another, but the sum of the kinetic and potential energy (also called total energy) remains the same. Work is the product of the displacement and the force in the direction of the displacement (force multiplied by distance). Whenever work is done, the energy of an object changes. Energy can be thought of as "stored work." Elastic potential energy (also called spring potential energy) is the energy of a spring due to its compression or stretch. The unit of work or energy is called the joule (J).
 * Physics Talk: Law of Conservation of Energy**

//Types of Energy & Formulas//

1. An unbalanced force is required for the energy of an object to change. 2. A penny being launched into the air receives its energy from the process of work. In our class's case, the work was the force of our hand upon the ruler holding the penny, giving it elastic potential energy. 3. Energies of food, kinetic, and elastic are present in a pole vaulter's performance. 4. Work and energy are defined in units called joules (J).
 * Checking Up Questions**

1. Work---> KE---> GPE ---> KE ---> Work 2. EPE---> KE---> Work 3. The vaulter could attain a height of 7.3m (1/2)mv^2=mgh (1/2)(12^2)=(9.8)h 72=9.8h 7.346=h 4. The length of the pole alone does not determine the limit of vaulting height. It also depends on external forces, especially initial velocity. 5. The temperature of some poles increases slightly as they flex. This would affect the performance negative, decreasing the vaulter's height. When heat is lost, the total energy left for potential is less. 6. Her speed was about 9.5m/s (1/2)mv^2=mgh (1/2)v^2=(9.8)(4.55) v= 9.5m/s 7. His speed was about 10.9m/s (1/2)v^2=(9.8)(6.14) v=10.9 8a. 8b. 9a. 9b. 10a. 10b. 11. 12a. 12b. 12c. 12d. 13. 14. 15. 16.
 * Physics To Go**

Initial Energy + Work in = Final Energy + Work out KEi + GPEi + EPEi + Win = KEf + GPEf + EPEf+ Wout
 * Law of Conservation of Energy: Notes**

Work in: force acting in direction of motion (Normal or tension) Work out: force acting in direction opposite of motion (Normal, tension, or friction) The amount of energy at the beginning should be equal to the amount of energy at the end.

Prompt: If champion pole vaulters can clear a 6.0-m high bar with a 5.5-m long pole, why can't they vault over a 12.0-m high bar with a pole 11.0 m long? What factors (variables) do you think limit the height a pole vaulter has been able to attain? Response: The energy present in the beginning of the situation must be equal to the energy present at the conclusion of the jump.
 * What do you think now?**

Section Nine
Prompt: Does the "hang time" of some athletes defy the pull of gravity? Does a world-class figure skater defy gravity to remain in the air long enough to do a triple axel? Response:
 * What do you think**

How much force and energy do you use to do a vertical jump? a. how much force and energy are needed to do a vertical jump b. the change in distance from the bent position to the unbent position, as well as the vertical height distance c. meter stick and force platform d. use the formula W=GPE and compare results to computer generated data Trial One Calculation: Win=GPE F(d)=mgh F(0.22)=(50)(9.8)(0.45) F(0.22)=220.5 F=1002
 * Investigate Section 9**
 * Trial Number || Change in Distance(m) || Vertical Height (m) || Weight (kg) ||
 * Trial One || 0.22 || 0.45 || 50 ||
 * Trial Two || 0.20 || 0.48 || 50 ||

Trial Two Calculation: Win=GPE F(d)=mgh F(0.20)=(50)(9.8)(0.48) F(0.20)=235.2 F=1176




 * Physics Talk: Conservation of Energy**

1. The energy is elastic potential energy. 2. In the launch position, gravitational potential energy and kinetic energy are present. At the peak of the jump, all of the energy is gravitational potential energy. 3. Types of energy besides gravitational potential energy and kinetic energy include work and elastic potential energy.
 * Checking Up Questions**

1. 2. 3. 4. 5. 6a. 6b. 6c. 6d. 7. 8. 9.
 * Physics To Go**

1a. GPE=KE+GPE mgh=(1/2)mv^2 + mgh m(9.8)(50)=(1/2)mv^2 +m(9.8)(30) (9.8)(50)=(1/2)v^2 + (9.8)(30) 490=(1/2)v^2 + 294 196=(1/2)v^2 392=v^2 19.8m/s= final velocity 1b. It is an advantage that the ride is mass independent because it simplifies the equation. 2. GPE+EPE= KE mgh + (1/2)kx^2 = (1/2)mv^2 (0.3)(9.8)(2) + (1/2)(60)(0.4)^2 = (1/2)(0.3)(v^2) (0.3)(9.8)(2) + (1/2)(60)(.16)=(1/2)(0.3)(v^2) 10.68=.15v^2 71.2=v^2 8.4m/s= final velocity 3. GPE + W = KE + GPE + W mgh + F(d) = (1/2)mv^2 + mgh + F(d) 200(9.8)(25) + 200,000 = (1/2)(200) (40^2)+ (200)(9.8)(h) + 50,000 249000 = 210000 +1960h 39000=1960h 19.9m= h
 * Physics Plus**

Prompt: Does the "hang time" of some athletes defy the pull of gravity? Does a world-class figure skater defy gravity to remain in the air long enough to do a triple axel? Response: It is physically impossible to defy gravity. The athletes, rather, are working //with// gravity to accomplish their incredible feats. The amount of energy must remain the same throughout the entire action due to the law of conservation of energy.
 * What do you think now?**