Chapter+2

Chapter 2 toc [|Article]

Curling is a fun sport to watch and engage yourself in. There are some "technical aspects" of this sport though, and in my article The Science Behind Curling, Pierre Baudin and Rob Krepps analyzed the best way to deliver a curling stone. They created a state-of-the-art research lab with motion analysis cameras and video cameras. Baudin and Krepps used advanced technology to gather as much information as possible about how to best deliver a curling stone. In the end, the two researchers discovered that there is no secret maneuvers to deliver a curling stone. "What really matters is what's happening with the line weight and rotation of the rock." All of these variables are important while curling but there is no way to purposefully enhance the movement of the curling stone. This is a good example of how physics and sports realte.

=Section 1 = What do you think? I think that figure skaters use a lot of force to make themselves move. They put in a lot of power in one push so it looks effortless. The soccer ball continues to roll across a field because of the force that was previously placed upon it before.

Investigate Make a hypothesis. Answer the question to the best of your ability at this time. **The vertical height would be the same on each side because the force exerted is equal** 1c. **5.33 meters** 1e. **5.31 meters** 2a. **His position on the opposite side of his initial position will be his highest point** 2b. **I think this because he has more room to "skate" and his slope was not decreased enough, he will be higher on the other side** 3a. **We were right because we changed the track and we knew the positions of the track.** 3b. **Vertical height of ball= 5.29 meters. The ball moved down the initial slope and then went up the other side to the exact same point as where it started but on the opposite side.** 4a. **Now that the slope is less steep he will not go up as high as his initial position on the opposite side** <span style="font-family: Arial,Helvetica,sans-serif;">4b. **I was wrong. He went almost a meter higher than where he started on the opposite side.** <span style="font-family: Arial,Helvetica,sans-serif;">5a. **No because he will never change direction** <span style="font-family: Arial,Helvetica,sans-serif;">5b. **He will keep rolling until the force behind him has completely decreased** <span style="font-family: Arial,Helvetica,sans-serif;">5c. **He would keep rolling** <span style="font-family: Arial,Helvetica,sans-serif;">5d. **My prediction was right. The skater eventually stops when the force behind him is gone** <span style="font-family: Arial,Helvetica,sans-serif;">6a. **The length of the opposite track increases** <span style="font-family: Arial,Helvetica,sans-serif;">6b. **It increases as the slope decreases** <span style="font-family: Arial,Helvetica,sans-serif;">6c. **It is the same.** <span style="font-family: Arial,Helvetica,sans-serif;">6d. **He would not stop since there was no friction** Physics Talk Summary Inertia is the natural tendency of an object to remain at rest or to remain moving with constant speed in a straight line. Newton's first law of motion is defined as 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. Mass is the amount of matter in an object. Galileo was a pioneer in the use of precise, quantitive experiments. He insisted on using mathematics to analyze the results of his experiments. Also, Isaac Newton credited him and others for their contributions to his thinking. Speed, velocity and acceleration were refreshed in our memories as well; defined, respectably, the change in distance per unit of time, speed in a given direction and the change in velocity per unit of time. A frame of reference is a vantage point with respect to which position and motion may be described.

Checking Up 1. **The natural tendency of an object to remain at rest or to remain moving with constant speed in a straight line** 2. **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** 4. **A certain force causes the ball to stop** 5. **The larger object will have a larger inertia** 6. **It is important to establish a frame of reference to know the perspective**

Physics To Go 1a. **It will roll forever** 1b. **If an object is in motion, it will continue to be in motion until a force acts upon it** 2. **20 cm** 3. **No because there is always friction** 4. **The puck will continue to move until another force acts upon it**
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">5. <span style="font-family: Tahoma,sans-serif; line-height: normal;">4.5m/s+2.5m/s=7m/s the ball is moving at the the person watching **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">6. <span style="font-family: Tahoma,sans-serif; line-height: normal;">10.3m/s+4.2m/s= 14.5m/s the javelin is moving relative to the ground **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">7a. <span style="font-family: Tahoma,sans-serif; line-height: normal;">5.6m/s+2.4m/s= 8m/s the cart is moving forward **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">7b. <span style="font-family: Tahoma,sans-serif; line-height: normal;">5.6m/s-2.4m/s= 3.2m/s the cart is moving backward **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">7c. <span style="font-family: Tahoma,sans-serif; line-height: normal;">Pythagorean theorem= 2.4^2+5.6^2=c^2=6.1m/s 23 degrees (tan inverse) **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">8. <span style="font-family: Tahoma,sans-serif; line-height: normal;">85m/s-18m/s= 67m/s the arrow is going **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">9. <span style="font-family: Tahoma,sans-serif; line-height: normal;">sin(angle)=opposite/hypotenuse **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">9a. <span style="font-family: Tahoma,sans-serif; line-height: normal;">sin(45)=15/x= 21 cm **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">9b. <span style="font-family: Tahoma,sans-serif; line-height: normal;">sin(20)=15/x= 44cm **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">9c. <span style="font-family: Tahoma,sans-serif; line-height: normal;">sin(15)=15/x= 58 cm **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">9d. <span style="font-family: Tahoma,sans-serif; line-height: normal;">sin(5) =15/x= 172 cm **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">10a. <span style="font-family: Tahoma,sans-serif; line-height: normal;">Rest: football sitting on a stand, waiting for someone to kick it. the glove of a baseball player waiting to catch the ball **
 * <span style="font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">10b. <span style="font-family: Tahoma,sans-serif; line-height: normal;">A sports caster would be dramatic while a football player sets up the football to kick a field goal and would say something like, "Here comes (player name), quickly running up to the ball to kick the field goal and it's good! Another point for (team name)!" **

What do you think now? Ice skaters seems to keep moving across ice at a high speed for a long tim, because the force behind them keeps them moving. They do not have an unbalanced force or an object in their way to make them stop, so the force that pushed them forward makes them move across the ice for this long period of time. A soccer ball continues to roll across the field after it is kicked, because who ever kicks the ball is usually running towards the ball, so that force along with the force of the kick is behind the ball, which makes the ball move across the field until the momentum or force runs out or until it hits another player on the field.

=Section 2= What do you see?
 * <span style="color: #000000; font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">I see two kids going at different speeds. The first boy is walking and than the dog in front of him is walking also. Than there is a snail in front of the walking dog. Also his steps are smaller. The second boy is running with flowers in his hand. Therefore the dog in front of him is running. His strides are bigger when running. **

What do you think?
 * <span style="color: #000000; font-family: Tahoma,sans-serif; font-weight: normal; line-height: normal;">100 mi/h is a speed that a baseball can go. This speed means that a baseball pitcher can throw a baseball 100 mi in the time of an hour. 45 m/s explains that in the matter of a second a pitcher can throw the ball 45 m. **

Physics Talk Summary <span style="font-family: Tahoma,sans-serif; line-height: normal;">During the investigate we explored constant speed and accelerations. We were able to tell whether the person pulling the tape was moving at constant speed or increasing or decreasing, and the acceleration during each time interval. One way to calculate motion is to calculate speed. Speed is the distance traveled to time taken. Average speed=distance traveled/time elapsed (v=d/t). When an object changes speed it is accelerating. Accelerating is the change of the speed divided by the time. It is also the change in direction of motion. Acceleration=change in speed/time interval (a=v/t). The units for acceleration are either (m/s)s or (km/h)s.

Checking Up 1a. **the dots will be an even amount of space away** 1b. **the dots will progressively get farther and farther away from each other** 1c. **the dots will progressively get closer and closer to each other** 2. **400 m/ 50 s = 8 m/s** 3. **Instantaneous speed is the speed at a given moment, where average speed is the total distance traveled divided by the time it took to travel that distance** 4. **1000 km/s / 10 s = 100 km/s**

Physics To Go 1. **Instantaneous speed is the speed at a given moment, where average speed is the total distance traveled divided by the time it took to travel that distance** 2a. **1000 m / 15 s = 66.7 m/s** 2b. **84 m/ 6 s = 14 m/s** 2c. **9.6 km / 2 h = 4.8 km/h** 2d. **400 km / 4.5 h = 88.9 km/h** 3a. **Negative** 3b. **Positive** 3c. **None** 3d. **Negative** 3e **None** 3f. **None** 4a. **A, D** 4b. **B** 4c. **A** 4d. **C** 4f. **None** 4e. **A +;** **B 0;** **C + then -;** **D +** 6a. **0-12 m/s / 9 s = 1.4 m/s^2** 6b. **Negative** 7a. **Constant** 7b. **Speeding up** 7c. **Constant, Speeding up, Constant** 7d. **Speeding up, Slowing down, Speeding up** 8. **100 mi / 2 h = 50 mi/h** 9. **No they could have had multiple speeds, but overall the average speed was 15 m/s** 10. **. . . . . .......** 11. **4, 8, 12, 16, 20 m/s** 14a. **Marathon Runner** 14b. **Car Races (indie 500)** 14c. **Walking around** 14d. **Football player running up to kick the ball** 14e. **Ending a race**

The meaning of 100 mi/ hi and 45 m/s is how fast you are traveling per second or hour. To me it means the movement of the wheels of the car plus the friction on the road are causing this.
 * What do you think now? **

<span style="color: #00127b; font: 13px/19px Arial; margin: 0px;">Physics Plus (X2) <span style="font: 13px/19px Arial; margin: 0px;">Rebounding- a bouncing off a surface and changing direction <span style="font: 13px/19px Arial; margin: 0px;">Assume acceleration is constant during the entire process
 * <span style="font: 13px/19px Arial; margin: 0px;">Velocity || <span style="font: 13px/19px Arial; margin: 0px;">Acceleration || <span style="font: 13px/19px Arial; margin: 0px;">Examples ||
 * <span style="font: 13px/19px Arial; margin: 0px;">Small || <span style="font: 13px/19px Arial; margin: 0px;">Small || <span style="font: 13px/19px Arial; margin: 0px;">golf cart ||
 * <span style="font: 13px/19px Arial; margin: 0px;">Small || <span style="font: 13px/19px Arial; margin: 0px;">Big || <span style="font: 13px/19px Arial; margin: 0px;">rebounding object ||
 * <span style="font: 13px/19px Arial; margin: 0px;">Big || <span style="font: 13px/19px Arial; margin: 0px;">Small || <span style="font: 13px/19px Arial; margin: 0px;">big truck ||
 * <span style="font: 13px/19px Arial; margin: 0px;">Big || <span style="font: 13px/19px Arial; margin: 0px;">Big || <span style="font: 13px/19px Arial; margin: 0px;">airplane ||



=Section 3= What do you think? A force is Venus' arm strength, the racket, and air. The same type of force will affect a bowling ball in the same way, but it will go slower because the ball is heavier.

<span style="color: #00127b; font: 13px/19px Arial; margin: 0px;">Physics Talk <span style="font: 13px/19px Arial; margin: 0px;">Newton's Second Law of Motion stated that the acceleration of an object is directly proportional to the unbalanced force action go it and is inversely proportional to the object's mass. The direction of the acceleration is the same as the direction of the unbalanced force. This is a mathematical way of saying that when the mass gets larger, the acceleration gets smaller (inverse proportion). To get a big acceleration, you need a large force to act upon a small mass. Acceleration= force/mass or A= F/m. Weight is the vertical downward force exerted on a mass as a result of gravity. It is a type of force and it can be calculated by F gravity﻿= ma gravity or w = mg. W is weight, m is the mass in kilograms and g is the acceleration due to gravity. A free-body diagram is a diagram that shows the forces acting on an object.

<span style="color: #000080; font: 13px/19px Arial; margin: 0px;">Checking Up <span style="font: 13px/19px Arial; margin: 0px;">1. **Newton's second law of motion states that acceleration is directly proportional to the force that acts upon the same object. It is also inversely proportional to the object's mass. The acceleration and unbalanced force act on the object in the same direction** <span style="font: 13px/19px Arial; margin: 0px;">2. **The acceleration decreases** 3. **There is 30 newtons of force acting upon the object** 4. **Your weight would be higher and your mass always stays the same**

Physics to Go ﻿1. "shaving ice" while stopping || -1500 N || 100 kg || ? **-15 m/s^2** ||
 * Sprinter beginning 100-m dash || ? **350 N** || 70 kg || 5 m/s^2 ||
 * long jumper in flight || 800 N || ? **80 kg** || 10 m/s^2 ||
 * shot-put ball in flight || 70 N || 7 kg || ? **10 m/s^2** ||
 * ski jumper going downhill before jumping || 400 N || ? **80 kg** || 5 m/s^2 ||
 * hockey player
 * running back being tackled || ?**-3000 N** || 100 kg || -30 m/s^2 ||

3. **42 N / .30 kg =** **140 m/s^2** 4. **20 m/s^2 X .040 kg =** .**8 N** 5a. **Throwing a baseball is easier than throwing a bowling ball because of it's weight and mass. The inertia of the objects are harder to change because of these two factors. If a bowling ball is at rest it will be harder to throw or to catch. A baseball is easier to throw and catch because it is smaller and lighter.** 5b. **You need more force to throw a bowling ball compared to a baseball. The unbalanced force will be the same but it will not be as effective for the bowling ball** 9. **Yes the force of your hand is still acting on the ball. It will stop acting on the ball when another unbalanced force act upon it. This is the situation considering there is no friction** 10. **40 N + 50 N =** **90 N** 11. **200 N X 4 = 800 N** 12. **(****a = f / m) 125 = .700 kg x; a** = **179 m/s^2** 13. **sqrt (120^2 + 50^2)****130 N at 67 degrees North East** 14. **sqrt (5000^2 4000^2);** **6430 N at 39 degrees** 15. **(****F = m x a)** **F = (12.8 kg) (9.8 m/s^2); F = 125.44 N** 16a. **sqrt (30^2 + 40^2);** **50 N at 53 degrees** 16b. **50 + (5.6) a; 8.9 m/s^2** 17a. **sqrt (30^2 + 40^2);** **36 N at 34 degrees** 17b. **36 = 100 X a; .36 m/s^2** 17c. **50 = 100 X a;** **0.5 m/s^2** 18. **The ball was tossed up at 10 m/s and it weighs 1 km so the force will be 10 N.**

Physics Plus 1. **125^2 + 125^2 = R^2 = 177 North East** 2a. **70 N - 40 N = 30 N South** 2b. **30^2 + 40^2 = 50 N** 2c. **A** **ngle = Tan-1 (30 / 40) = 37 South East**
 * Angle = Tan-1 (125 / 125) = 45 degrees**

What do you think now?
 * A force is a push or a pull on an object that causes acceleration. If a large force is exerted on to a tennis ball then there will be a large acceleration. If the same amount of force is exerted on a bowling ball, it will have less of an acceleration because the mass is much greater than a tennis ball. **

=Section 4= What do you think? The force exerted on an object, gravity, the angle it was thrown at and how heavy the object is determines how far an object is thrown.

Investigate Part A 1a. **Yes they hit the floor at the same time** 2a. **They hit the floor at the same time** 3a. **No because it has the same acceleration and velocity** 3b. **Yes it goes out more horizontally but they still hit the floor at the same time** 4a. **No it will go horizontally for a longer period of time**

Investigate Part B 5a. **It will probably fall behind the thrower** 6a. **The vertical component of the velocity decreases on the way up. The vertical components of velocity increase on the way down. For the most part, the horizontal components of velocity do not change.** 6b. **Speed and the trajectory of the objects affect the range of the ball**

Investigate Part 3 1. **As horizontal launch velocity was increased so was the time in the air** 2. **As the horizontal launch velocity increased so did the range** 3. **As initial height was increased so did the time in the air** 4. **When initial height was increased the range also increased** 5. **The initial speed will affect the flight of a projectile** 6. **The initial speed and heigh influence range of projectile**

Physics Talk Summary Projectile is an object traveling through the air or other medium. The horizontally thrown coin and the dropped coin hit the ground at the same time when there is little or no air resistance. Horizontal movement does not affect the downward motion. Any hit or thrown ball travels horizontally and vertically. The horizontal velocity remains the same if there is no air resistance. Needs to be Ay= 9.8 m/s^2 or Ax= 0 (NOT A PROJECTILE IF THESE AREN'T TRUE) Trajectory is the path of the projectile (ground to ground are symmetrical around the highest point). X and Y information are independent from each other When an object "free falls" the only force is the weight but its one dimensional motion (vertical only). The vertical position on free fall and projectile are the same.

Checking Up ﻿1. **Yes** **because there is no air resistance and they have the same gravitational pull.** 2. **Yes by 10 m/s every second** 3. **The velocity is 0 at it's highest point and the acceleration 9.8**

Physics Plus

What do you think now? ** It all depends on the hight that the object was thrown and the speed of the object throwing it **

Physics to Go 4. **People thought that the coins would hit the ground at different time because one coin travels horizontally as well as vertically. What they don’t know is that the vertical and horizontal velocity is equal.** 6. **In class, we did the experiment multiple times and the two coins always hit the ground at the same time. We also used distance equations that mathematically proved our observations true.** 7. **The arrows will both hit the ground at the same time because they have to travel the same vertical distance.** 8. **The swimmer’s velocity is 1 km/h because of the current** 11. **And once again, the pitcher winds up, and releases the ball. Holy mackerel did you see that fast ball? Not fast enough for our speedy batter. The ball just flew over the left fielder! Seems like he should have though more about the velocity of this ball because the other team just got a double!**

Reflecting on the Section Sports Video: [|Reflecting on the Section] During the time of this video from about 24 seconds until about 36 seconds you see a basketball player running down the court to throw a basketball int he net. The ball had a lower horizontal velocity compared to the vertical velocity therefor the ball went into the net. Also the angel that the ball was thrown at as well as the force exerted on it played a role.

=Section 5= What do you think? When the angel is changed the trajectory will also change. A greater launch speed can cause the range to become larger because the same object is going at a faster velocity. When the launch angel is smaller the time in the air is also smaller.

Physics Talk Summary Trajectories of projectiles can be modeled using a computer or graphing calculator. Launch angel, launch speed, launch height, and range are variables that are able to be manipulated. All balls travel in parabolas. The distance traveled at pairs of angels are identical. Small angels have greater horizontal velocities but are in the air a short time. Large angels have smaller horizontal velocities but are in the air a long time. During ground to ground launches, complementary angels have the same range. 45 degrees has the greatest range. Between 0 degrees and 45 degrees has the largest range (x-component).

Checking Up 1. **The two types of motions are vertical and horizontal** 2. **The scientific model must match a model in nature** 3. **The distance angels traveled at pairs are identical in all parabolas.**

Physics Plus

What do you think now? When the angel is changed the trajectory will also change. A greater launch speed can cause the range to become larger because the same object is going at a faster velocity. When the launch angel is smaller the time in the air is also smaller.

Physics to Go 1. **45 degrees because the object will go the farthest it can.** 2a. **The bigger then angle is that is greater than 45 degrees, the less far the object will go** 2b. **As the angle gets bigger before it hits 45 degrees, the object will go farther.** 3a. **90- 30 = 60 degrees** 3b. **90- 15= 75 degrees** 4. **I think this occurs because most people can run faster than they can jump high. If she runs really fast before hand, she will have a bigger range without jumping at a 45 degree angle.** 5. **I think that he was successful in his events because if he goes his highest velocity. He has a great horizontal velocity when he is running before hand and he is also good at launching himself upward at a fast speed.** 6a. **The balls acceleration is -9.8 m/s squared.** 6b. **The direction of the balls velocity at point x is downward.** 7a. **V= Vi +at** 7b. **15 = Vi (1)** 7c. **d = Vi t** 8. **The angle would have to be 45 degrees to travel the farthest distance.** 9. **The biggest angle would be close to 90.** 10a. **The acceleration is downward. (-9.8 m/s squared)** 10b. **d = Vi t + 1/2 a t^2** 10c. **d = Vi t + 1/2 a t^2**
 * (-9.8) (3) = 29.4 m/s**
 * Speed: 29.4 m/s**
 * 5 m/s**
 * d = 15 meters**
 * -100 = -4.9 t^2**
 * t = 4.5 seconds**
 * d = 20 (4.5)**
 * d = 90 meters**

=**Section 6**= What do you think? To jump, you need to bend your knees slightly and push off your feet as hard as you can to jump high. There needs to be enough force to push the weight of your body off the ground. The force in the ground is equal to the force that you are exerting on it. The boy in the picture is pushing really hard off the wall so he will go very fast and very far.

Physics Talk Newton's third law of motion states that forces come in pairs; the force of object A on object B is equal in strength and opposite in direction to the force of object B on object A. A free body diagram is a diagram showing the forces acting on an object. They can be used to show the different forces. A center of mass is the point at which all the mass of an object is considered to be concentrated. A big mass as a small acceleration and a small mass has a big acceleration. Gravity is a pulling force

Checking Up 1. **Newton's third law of motion states that if one object acts on another, the same amount of force is transfered between the two objects.** 2. **Since earth pulls down a certain mass with the force of gravity, gravity is also acting upon the earth, pushing objects that are pushing up, down.** 3. **A free body diagram illustrates the different forces acting upon an object**

Physics Plus

What do you think now? You need to push with your feet enough force to make the ground push the force you exerted back. The force you apply must be down so the earth's force pushes you back up.

Physics To Go 1. **Yes, due to Newton's third law** 2. **The chairs are not intelligent, but the gravity of the earth pushes the same force that is being exerted on the chair** 3. **The scale measures the pressure that you put on the scale and a spring pushes back equal force**. 4. **The bat could break because the force the ball exerts is much greater than the bat does. Another reason is that the force exerted for the bat could be too great for the ball.** 5. **They will not exert equal forces because they are two different sizes and accelerate differently. They also have different masses.** 6. **The boards deflect each other when a large force hits them. The heavier player pushes on the board but is pushed back at a great acceleration because of it's original high speed.** 7. **A baseball player has a better chance of equalizing the force exerted by the ball when wearing a glove because it is bigger and stronger than a human hand.** 8a. **The bat weighs 2 pounds, traveling at 80 miles per hour. He put a total of 1,110 newtons of force into the swing, between the movement of the hips to the movement of the hands and wrists. The ball weights 145 grams. He drove that ball out of the park! The acceleration of the ball was 7.65 m/s^2.** 8b. **When a heavy ball hits a soft ground, the ground can deflect the ball and it will bounce back up off the ground.**

=**Section 7**= What do you think? Some sports require certain shoes because of where the sport is being held. There might be more or less friction so the athlete will need a shoe to accommodate the friction.

Physics Talk µ:
 * coefficient of friction
 * no unit
 * ratio of friction force to normal force
 * measure of how much 2 surfaces interact when sliding
 * 0 < µ < 1
 * µ bigger when surface is rough
 * independent of weight
 * it is only valid for a particular pair of surfaces

Lab

__**Part One**__ 1. **Weight of the block is 2 N** Average Tension: 3.93 N
 * Tension (N) || Ff (N) || Total Weight (N) || µ || Class Average µ || % Difference ||
 * 4 || 3.8 || 4 || 3.93 || 12 || .33 || .332 || .60% ||

//Sample Calculations:// ∑Fx = max ∑Fy = may µ = F/N T - //f// = 0 N - w = 0 µ = 3.93 / 12 T = //f// N = w µ = .33 N = 12

__**Part 2**__
 * Mass (g) || Mass (kg) || Measured Time (s) || Measured Distance (m) || Ff (N) || Acceleration (m/s^2) || Calculated v (m/s) || Calculated time (s) || % error ||
 * 183.72 || .1837 || 1.25 || 3.8 || 3.93 || -3.21 || 4.93 m/s || 1.55 || 19% ||
 * 183.72 || .1837 || 1.08 || 2.75 || 3.93 || -3.21 || 4.00 m/s || 1.25 || 13% ||
 * 183.72 || .1837 || 1.11 || 3.5 || 3.93 || -3.21 || 4.47 m/s || 1.50 || 26% ||

//Sample Calculations:// ∑Fx = max ∑Fy = may µ = F/N Vf^2 = Vi^2 + 2ad -//f// = .1837a Nf - w = may .33 = F/2 0 = Vi^2 + 2(-3.21)(3.8) -.59 = -.1837a Nf - 2 = 0 F = .59 SQRT 24.4 = SQRT Vi^2 a = -3.21 Nf = 2 Vi = 4.93

Checking Up Questions 1. **You can say they are equal to each other because the force reading on the spring-scale is coming from the shoe sliding across a friction-filled surface.** 2. **It has no units because it is dividing Newtons by Newtons, which cancel each other out.** 3. **The coefficient of friction is determined by the equation mu (force of friction / normal force)**

Active Physics Plus
 * tan(30) = .577 =** //**f**//**s**
 * X / 1.5 (9.8) = .577**
 * X = .577 (9.8) (1.5)**
 * X = 8.48 N**

Physics To Go 1. **During track a runner will want to increase friction between the floor and their shoes to decrease the chance of him falling during a race. During conditions such as snow or rain, the runner might need a different type of shoe to create more friction on the track.** 2. **Athletes desire the least amount of friction during ice skating to let them slide gracefully across the ice without friction causing them to get stuck in the ice.** 3. **The basketball player cannot be sure because she needs to know the type of service the other court has and the amount of friction that the surface exerts.** 4. **Tennis players have shoes for different surfaces to make sure that they have a good amount of friction no matter what court they are on.** 5. **∑Fx = max**
 * N - w = 0**
 * N = w**
 * N = 600**


 * µ =** //**f**//**/N**
 * .03 =** //**f**//**/ 600**
 * 18 N =** //**f**//

6a. **w = mg**
 * w = 1000 (9.8)**
 * w = 9800 g**

6b. **µ =** //**f**//**/N**
 * .55 =** //**f**//**/ 9800**
 * 5390 N =** //**f**//


 * ∑Fy = may**
 * N - w = may**
 * N - 9800 = 0**
 * N = 9800 N**

6c. **∑Fx = max**
 * -**//**f**// **= max**
 * -5390 = 1000a**
 * -5.39 m/s = a**

6d. **Aav = Delta v/ t**
 * -5.39 = Delta v/ 6**
 * -.9 = Delta v**

6e. **Vf = Vo + at**
 * 0 = Vo -5,39 (6)**
 * 32.34 m/s = Vo**


 * Obviously the driver was lying because he said he was driving at 29 m/s when he was actually going 32.34 m/s**

7. **I think that both air resistance and water resistance change directly with the speed that you are going.** 8. **If there is maximum frictional force between your shoe and the track, it will effect how fast you can accelerate because the more friction there is between the two objects, the slower the track runner can accelerate. To take away this problem, the track runner needs to find shoes that exert the least amount of friction.** 10. **Friction is important when you run because it keeps you from sliding. Cleats are used because it causes more friction when you run** 11. **"Here comes Johnson up to bat! he swings and dashes to first base, then second base! will he stop on the base or go over? If his shoes apply allot of friction he will slow down in time!**

What do you think now? **Some sports require special shoes because of the way the players reacts to the ground they are on. Depending on the kind of surface they are on, the more, or less, friction they will need, which will be given to them with various shoes.** **Cleats are helpful for soccer because they keep you balanced and add friction so you don't slip. Ice skates are best for the ice because you can glide on them due to their ability to lessen friction.**

=Section 8= What do you think? The factors that limit the height of a pole can be the weight of the person, weight of the pole, how far and high the person has to jump and climate.

Investigate Pre lab: A. **To blast the penny in the air we are going to pull down the end of the ruler that is hanging off the table and release** B. **Factors of the ruler that will affect our experiment will be the deflection of the ruler (force, elasticity), length of the ruler, placement of the penny and mass of the object**.

1a. **We will be able to conclude that length of the ruler hanging off the table will directly or directly relates to the height of the launched penny** 1b. **We will record the height of the penny and compare it to the amount of the ruler that is hanging off the table** 1c. **A penny, a ruler and a meter stick will be the tools we are using the make our measurements** 1d. **We will record it in a data table and compare the two variables to each other** 2.
 * **Trial** || **Height of Penny (cm)** || **Length of Ruler (cm**) ||
 * **1** || 60 || .5 ||
 * **2** || 110 || 1 ||
 * **3** || 130 || 1.5 ||
 * **4** || 165 || 2 ||
 * **5** || 180 || 2.5 ||
 * Conclusion**: The height of the penny depends on and is directly proportional to how far the ruler is off the table. When more ruler is hanging off the table, the penny goes higher.

Physics Talk Potential Energy is the energy associated with position.

__**Law of Conservation of Energy**__ is a law that states that energy cannot be created or destroyed; it can be transformed from one form to another, but the total amount of energy remains constant. Initial Energy + Win = Final Energy + Wout Initial Energy: KEi + GPEi + EPEi Final Energy: KEf + GPEf + EPEf KEi: Vi > 0 (moving) GPEi: h > 0 (above the "ground") EPEi: spring compressed at start Wi: must be a force acting in the direction of motion (N or T force)

KEf: Vf > 0 (moving) GPEf: hf > 0 (above the ground) EPEf: spring compressed at the end Wout: acts in the opposite direction of motion (N, T, or F)

when it is moving || KE = 1/2 m V^2 || when it is above its lowest point || GPE = mgh (how far some weight is lifted) || when stretched or compressed || EPE = 1/2 //k// x^2 //k// = spring force constant x = stretched/compressed distance || some distance **parallel to the** "energy", but it creates it. || W = F*d ||
 * **Types of Energy** || **Description** || **Equation** ||
 * Kinetic Energy || Energy possessed by an object
 * Gravitational Potential Energy || Energy possessed by an object
 * Elastic Potential Energy || Energy possessed by a string
 * Work || Caused by a force acting over
 * direction of motion.** Not really

Kinetic Energy is the energy associated with motion. Gravitational Potential Energy is the energy an object possesses because of its vertical position from Earth.

Work is the product of the displacement and the force in the direction of displacement. Elastic Potential Energy (spring potential energy) is the energy of a spring due to its compression or stretch

Checking Up 1. **Another force acting upon the object** 2. **The ruler pushing it up** 3. **Food gives the pole vaulter the ability to create more kinetic energy. They use this energy to bend the pole and the EPE causes the pole to go back straight and throw the pole vaulter over the pole. GPE increases as height increases.** 4. **Work: W** **(W=Fd)**
 * Kinetic Energy: KE** **(KE= (1/2)mv^2)**
 * Gravitational Potential Energy: GPE** **(GPE=mgh)**
 * Spring Potential Energy: EPE** **(****EPE=(1/2)kx^2****)**

Physics to Go ﻿1. **W --> KE --> GPE --> KE --> W** 2. **EPE --> KE --> W --> KE --> GPE** 3. **1/2mv^2 = mgh** **1/2m (12^2) = m (9.8) h** **1/2(144) = 9.8h** **7.35 meters = h** 4. **Because velocity and work are more important pieces of information** 5. **If the temperature increases then height decreases** 6. **1/2mv^2 = mgh** 7. **KE = GPE** 8a. **GPE = KE** 8b. **No, because the weight of the rock depends on how fast it will fall** 9a. **W = EPE** **W = ½ kx^2** **W = 47J** 9b. **EPE = KE** **47 = ½(.1)v^2** **31 m/s = v** 10a. **W = EPE** **W = ½ kx^2** **W = ½ (315)(.3)^2** **W = 14.2J** 10b. **Fd = ½ kx^2** **F(.3) = 14.2** **F = 47.3 N** 11. **EPE = GPE** **½ kx^2 = mgh** **½(18)x^2 = (.04)(9.8)(1)** **x = .21 m** 12a. **F = ma** **N = kg (m/s)^2** 12b. **GPE = mgh** **GPE = kg(m/s)^2** **GPE = N x m** 12c. **KE = ½ mv^2** **KE = kg(m/s)^2** **KE = N x m** 12d. **EPE = ½ kx^2** **EPE = (N/m)(m^2)** **EPE = N x m** 13. **EPE to KE to GPE to Work out** 14. **Work in to KE to GPE** 15. **The player that swings the bat and hits the ball does initial work. The ball goes flying with kinetic energy. This is done until work its outputted by the ground or another player catching the ball.** 16. **The sport we are using in our voiceover is going to be a mix of baseball and softball. The question above directly relates to our chapter challenge**
 * 1/2 v^2 = 9.8 (4.55)**
 * v = 9.6 m/s**
 * 1/2 mv^2 = mgh**
 * 1/2 v^2 =9.8(6.14)**
 * v= 11 m/s**
 * mgh = 1/2 mv^2**
 * 9.8 (100) = 1/2 v^2**
 * v = 44.2 m/s**

What do you think now? The length of the pole does not affect how high or how fast the person goes. The KE of the vaulter determines the height and distance as well as the GPE and work put into the push of the pole.

=Section 9= What do you think? If the correct amount of force was applied to the ground that the person is pushing themselves off of, it may be possible for them to stay in the air compared to a person that is simply jumping. They are using more force so they will go higher, faster and stay in the air longer.

Physics Talk Position V || EPE || GPE || KE || Work done is equal to the product of the applied force and the distance. Energy is transfered through EPE, GPE and KE until the energy reaches another object
 * Energy ->
 * Ready Position || maximum || 0 || 0 ||
 * Launch Position || 0 || some || maximum ||
 * Peak Position || 0 || maximum || 0 ||

Investigate: __Pre Lab__ 2. **The skater is in the air for 20 frames at 1/30th of a second** 3. **The amount of time in the air is 2/3 seconds** 4. **The skater did not actually hang in the air. Hang time is not real.** 5. **Basketball player was in the air for 30 frames or 1 second.**

__Lab__ 1a. **Work and gravitational potential energy are exerted when I jump** 1b. **We will record starting hip point, bent hip point, and the distance between ground and shoes when at the highest point in the air.** 1c. **A meter stick** 1d. **We will put the data in to the equation Fd = mgh** __Calculations__ Fd = mgh F(.25) = (611.04)(1.15) F = 2810.8
 * Trials || Initial Hip Height || Bent Hip Height || Distance between floor and feet ||
 * 1 || .93 m || .68 m || .9 m ||
 * 2 || .93 m || .64 m || .17 m ||
 * 3 || .93 m || .60 m || .20 m ||

Fd = mgh F(.29) = (611.04)(.46) F = 969.2

Fd = mgh F(.33) = (611.04)(.53) F = 981.4



Checking Up 1. **The energy that allows the jumper to move from the ready position to the launch position comes from the EPE of his mussles** 2. **In the launch position you have PE and EPE. During the peak of the jump they will have KE and GP** 3. **Three other types of Energy: gravitational, elastic, and static.**

Physics to Go 1. **W = Fd** 2. **Win + GPE --> Ke** **à** **Wout** 3. **To show someone that hang time does not really exist you can do what we did in class: freeze each frame at 1/30****th** **of a second and show the movement.** 4. **The person who is making the claim needs to prove it through evidence that can be shown to everyone and have an experiment with different variables.** 5. **You need to increase force and reduce body mass.** 6a. **W = 1 J** 6b. **W = 10 J** 6c. **W = 10 J** 6d. **W = 10 J** 6e. **W = 10 J** 7a. **GPE = 1 J** 7b. **GPE = 10 J** 7c. **GPE = 10 J** 7d. **GPE = 10 J** 7e. **GPE = 10 J** 8a. **KE = 1 J** 8b. **KE = 10 J** 8c. **KE = 10 J** 8d. **KE = 10 J** 8e. **KE = 10 J** 9.**W = Fd** 10.**KE = ½ mv^2**
 * W = 50(9.8)(1)**
 * W = 490 J**
 * W = (50)(43)**
 * W = 2150 J**
 * KE = ½ (62)(8.2^2)**
 * KE = 2084.44 J**

11a. **A = F/m** 11b. **W = F/d** 12a. **W = Fd** 12b.**A = F/m** 13. **W = KE** 14. **W = KE**
 * A = 30/5**
 * A = 6 m/s^2**
 * W = (30.00)(18.75)**
 * W = 563 J**
 * 40,000 = 3,200d**
 * d =12.5 m**
 * A = 3,200/1,200**
 * A = 2.7 m/s^2**
 * W = 1/2 mv^2**
 * W = 1/2 (.15)(40^2)**
 * W = 120 J**
 * W = 1/2 mv^2**
 * W = 1/2(64)(40^2)**
 * W = 7,200**

15. 16.
 * W = Fd**
 * 7,200 = 417d**
 * d = 17 m**
 * || KE || GPE || EPE || Sum ||
 * Running || 100 J || 0 || 0 || 100 ||
 * Full bend of pole || 10 || 0 || 90 || 100 ||
 * Peak Height || 0 || 100 || 0 || 100 ||
 * Landing || 80 || 20 ||  || 100 ||
 * Cushion Collapse ||  || 20 ||   || 0 ||
 * || KE || GPE || EPE || Sum ||
 * Peak Height || 0 || 1000 || 0 || 1000 ||
 * Landing || 800 || 200 || 0 || 1000 ||
 * Lowest Height || 0 || 0 || 1000 || 1000 ||

17. 18. **The crowd goes quiet as the pitcher puts work into the ball, causing it to move with kinetic energy. The GPE of this object needs to be around the waist of the batter in order for the pitcher to throw a strike.**
 * || KE || GPE || EPE || Sum ||
 * Top of Mountain || 0 || 1000 || 0 || 1000 ||
 * Middle || 500 || 500 || 0 || 1000 ||
 * Bottom || 1000 || 0 || 0 || 1000 ||

Active Physics Plus 1a.**GPE = KE + GPE** 1b. **It is an advantage because we only have to solve for one variable**
 * mgh = ½ mv^2 + mgh**
 * 9.8(50) = ½ v^2 + (9.8)(30)**
 * 490 = ½ v^2 + 294**
 * 396 = v^2**
 * 19.8 = v**

2. **GPE + EPE = KE** 3. **GPE + Win = KE + GPE + Wout**
 * mgh + ½ kx^2 = ½ mv^2**
 * (.3)(9.8)(2) + ½ (60)(.4^2) = ½ (.3)v^2**
 * 10.68 = .15v^2**
 * 8.4 = v**
 * mgh + Fd = ½ mv^2 + mgh + Fd**
 * (200)(9.8)(25) + 200,000 = ½ (200)(40^2) + (200)(9.8)h + 50,000**
 * 249,000 = 210,000 + 1,960h**
 * h = 19.9 m**

What do you think now? No the "hang time" is not actually real. Energy is transfered in comparison to time and space from one object to another. Work is put into doing something causing any type of energy (kinetic, gravitational potential, or elastic potential) that is transfered from one object to another which causes the motion of an athlete. In the beginning of the section, we watched two different sports actions (a figure skater and a basketball player) and froze the time every 1/30th of a second. We found that there is no such thing as hang time and that there is energy transfered at every single point in time.