Physics+in+Action-Chapter+2

toc =** Nichole Formicola's Wikilog - Period 8 CP Physics - E. Burns - 2010 **=

CHAPTER 2: SECTION 1
//The Science Behind Curling// by: University of Alberta [|Link]
 * __ Sports Article 11/7/10 __**

__**Summary:**__ The article that I read was about the sport curling. Curling is an Olympic sport involving ice. What you do in the sport is you push a ball on the ice and than your other teammates brush the ice so that the ball goes farther. There are many 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. The University of Alberta created a state-of-the-art research lab with motion analysis cameras and video cameras, to analysis the sport. 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. The only thing that can really enhance the farther your curling stone goes is the friction between the ice and and the stone.

__** WHAT DO YOU SEE: **__ __** 10/8/10 **__ I see kids playing soccer. It is showing how different forces effect the balls distance. There is a bug pushing and ball and it is showing its not moving and same with the rat. Than there is one kids who taps it and it only moves a few feet. Than there is a couple other kids running up to the ball showing that the more speed and force behind an object the farther the object with carry.

Figure skaters keep moving across the ice for a long period of time, because the force behind their push carries them. Also, ice and the skate allow the skater to keep moving, because the surface is slippery. A soccer ball continues across a field after it has been kicked, because the force behind the ball carries the ball across the field and it will keep rolling until the force dies out. There is still momentum.
 * __ WHAT DO YOU THINK: __**

__** INVESTIGATE: NEWTON'S FIRST LAW: **__ __** 11/8/10 **__ __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 .  ** Initial:5.75m **  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.

__2. Change the position of the last blue circle to decrease the slope of the opposite track, but make sure that its end it still at least as high as the first blue circle.__ a) Predict where the skater will reach his highest position if he begins at the same place as before. !  I think that the position will be higher.  b) Explain why you think so. !  I think this because the slope is decreased, so it does not have to go up so high.

__3. Press play. (Note: if at any time you need to zoom out, because you can’t see the end of your track, click the magnifying glass with the minus sign. The screen will adjust to fit your track.)__

a) How close was your prediction to the actual outcome? Why do you think your prediction was “close” or “way off”? ! My prediction was off, because I thought that the skater would go higher, but it looks as if he went the same height. 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. ! The distance was 5.75m. The ball first started off at 5.75m for its initial height. When I moved the blue circle and pressed play, the ball on the other end of the ramp went to the exact same height as the initial.

__4. Repeat Steps 2 and 3, creating an even less steep slope.__ a) First record your prediction. ! I think that it will stay the same based on what I learned from step 3 b) Compare your prediction with the outcome. ! the outcome was what I predicted

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? ! No he would not recover his starting height, because now the surface is flat and in a straight line. The skater is just rolling along a flat ground. b) How far do you think the skater would roll? ! I think that the skater would roll farther now, because the ground is flat so it does not have to go up a height, so his momentum and force keeps going with him until it dies out. c) What would keep the skater rolling on a horizontal track? ! The force from the initial drop and height . d) Try this on the simulation. What happens? ! The skater keeps going straight, and goes a farther distance until it falls of the track.

__6. Conclusion Questions:__ a) What happens to the length of the opposite track the skater rides as the slope decreases? ! It starts to straighten out and the slope decreases. The length increases b) What happens to the final vertical position on the opposite track the skater rides as the slope decreases? ! As the slope decreases than the position stays the same, but once you make the slope zero, than there is no height. 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? ! They are both directly related, because they are both the same height if there is a slope. If there is no slope than the heights are indirectly related, because there is no height to calculate, there is only distance. d) If the opposite track was infinitely long, and frictionless, when would the skater stop? ! The skater would stop when the force died out or it will never stop, it will keep rolling.

__**Summary:**__ Galileo performed an experiments and he concluded that, "the ball would continue its motions on the horizontal surface with constant speed along a straight line to the horizon." He w as the first one to question the catholic church. Also he practiced an experiment where he rolled a ball down one ramp to see if it rolled to the same height on the other. From these two experiments he created 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. Force is a push or a pull. Isaac Newton created Newton's First Law of Motion which stated that in the absence of an unbalances force, and object at rest remains at rest, and an object already in motion remains in motion with constant speed in a straight-line path. An objects mass i a measure of its inertia. The one with the greatest mass has the greatest inertia. The kilogram is the base unit of mass, which is equal to 1000 grams. Velocity is speed in a given direction. Frame of reference is a vantage point with respect to which position and motion may be described. Inertia is a property of mater that resists changes in motion. Mass is how much matter something has, this is what inertia is measured in. Running starts increase distance and speed to give advantage. Frame of reference if you are on a plane to everyone else inside you look like your not moving, but to people on the ground you would look like your going 400mph. Relative to another object, adding or subtracting velocities.
 * PHYSICS TALK: PG 134-138 **
 * 11/8/10 **

1) Inertia is the natural tendency of an object to remain at rest of to remain moving with constant speed in a straight line. 2) Newton's First Law of Motions 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. 3) external force 4) The frictional force, which is the force that you cannot see stops the object. 5) The object with the greater mass will have bigger inertia. 6) To describe the perceptive your looking from.
 * CHECKING UP QUESTIONS: **

1a) The ball will roll until the momentum runs out or until it hits something it will run forever 1b) You cannot tell exactly when it will stop, unless you know where or when it comes in contact with an unbalanced force 2) It would reach 20 cm on the opposite side of the ramp and than come back down. 3) No I don't think this is possible because if an object was able to stay at a constant speed than there would be things hitting into each other everywhere. I don't think this is possible because than there would be no force in the world. No friction in the world. 4) When the stick hits the puck, the force behind the puck is so strong, that the puck will keep going until it hits something. When it hits something at full speed, than it will probably bounce back, because the force behind it is so strong. Also, because you pull your arm up to hit the puck the force is even stronger. 5) 4.5m/s+2.5m/s=7m/s the ball is moving at the the person watching 6) 10.3m/s+4.2m/s= 14.5m/s the javelin is moving relative to the ground 7a) 5.6m/s+2.4m/s= 8m/s the cart is moving forward 7b) 5.6m/s-2.4m/s= 3.2m/s the cart is moving backward 7c) Use Pythagorean theorem= 2.4^2+5.6^2=c^2=6.1m/s 23 degrees (use tan inverse) 8) 85m/s-18m/s= 67m/s the arrow is going 9) sin(ANGLE)=opposite/hypotenuse 9a) sin(45)=15/x= 21 cm 9b) sin(20)=15/x= 44cm 9c) sin(15)=15/x= 58 cm 9d) sin(5) =15/x= 172 cm 10)
 * PHYSICS TO GO: **

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.
 * WHAT DO YOU THINK NOW: **
 * 11/10/10 **

REFLECTING ON THE CHALLENGE AND SECTION:
 * 3 links:**


 * INQUIRING FURTHER **

** CHAPTER 2: SECTION 2 **

 * 10/11/10 **

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 SEE: **

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.
 * WHAT DO YOU THINK: **

Summary: 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= change in distance traveled/change in time (v=d/t). How fast position changes, and large distance or times over which there may be variations. 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)(vf-vi/t). The units for acceleration are either (m/s)s or (km/h)s. Positive acceleration is increasing speed, negative acceleration is decreasing speed. When v and a have the same signs its increasing speed, when v and a have opposite signs its decreasing speed.
 * PHYSICS TALK: **

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. 400m/50s = 8m/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.a-100-0/0.0028h=36000km/h^2 remember to change units cannot have different measurements combined
 * CHECKING UP QUESTIONS: **

Physics To Go 1. Instantaneous speed is the speed at a given moment. Average speed is the total distance traveled divided by the time it took to travel that distance. 2a. 1 km / 15 s = 0.06666 km/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 and D 4b. B 4c. A and C and D 4d. C 4f. None 4e. 6a. -450 m / 1s = -450 m/s. the vehicle negatively accelerated at a rae of -450 m/s 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. They could have had multiple speeds, but overall the average speed was 15 m/s 10. . . . . . ....... 11. 14a. Swimming 14b. Soccer 14c. Dance 14d. Football 14e. Diving
 * PHYSICS TO GO: **

PHYSICS PLUS (X2) p 152 small 1m/s big big || small 1m/s^2 big 10m/s^2 small big || 0-1-2-3-4=Golf Cart, jogger, 10-20-30-40= rebounding objects big truck airplane || __**Rebounding**__: changing directions, bouncing off a surface and changing direction. Assume that the acceleration is constant throughout the entire process ex: when a ball is dropping to the ground (-Vi) and it gets compressed until stops and than it bounces back up (Vf) because they compression releases. 1) a=Vf-Vi/t Vi=.5m/s Vf=.5m/s T1=1 s a=.5-(-.5)/1=1m/s^2 T2=0.1s a=.5-(-.5)/.1s=10m/s^2 T3=.01s a=.5-(-.5)/.01s=100s
 * Velocity || Acceleration || Examples ||
 * small 1m/s

2) Vi=.5m/s Vf=.5m/s T=.20s a=.5m/s-(-.5m/s)/.20s=5m/s^2

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. These two are measurements of distance in a certain amount of time. This is the average speed, because it included distance and time. 45m/s means that an object can go the distance of 45 meters in 1 second. 100mi/h means that an object can go the distance of 100 mi in 1 hour.
 * WHAT DO YOU THINK NOW: **

** CHAPTER 2: SECTION 3 **
A force is the energy or strength an object has behind it. The same amount of force will act differently because of the weights. Since a tennis ball is a lot lighter and bouncier the tennis ball with move faster. Since the bowling ball is heavier it will not go as fast as a tennis ball. You would need a lot more force, and also it does not rebound. i see the same person going three different speeds pushing a ball. Than I see a dog going three different speeds. An observation is information that you get through your senses. When you describe the qualities of objects, events or processes observations are qualitative. (smells spicy, tastes sweet). Observations based on measurements or counting are quantitative. (sauce temperature on stove) Newtons Second Law of Motion can be written as acceleration=force/mass (a=f/m). Force is expressed in Newtons in the second law. A newton is a derived SI unit with a special name. A newton is a force required to make on kilogram of mass accelerate at one meter per second squared. a newton=1kg(m/s^2). There are many different types of forces such as, the force of a spring, the forceof a rubber band, the force of a magnet, the force of you hand, the force of a bat hitting a bal, the force of friction, and the buoyant force of water. Newtons second law tells you that accelerations are caused by unbalanced forces. Also, it does not matter what kind of force it is or how it originates. When you apply a force to an object that has a small mass, the acceleration might be quite large, if the object has a large mass, the acceleration will be smaller or the same force. (if the mass is to big than you might not even be able to measure the acceleration because its to small.) For example if you push a truck, the acceleration would be so small to measure. Sig Figs All nonzero numbers are considered to be significant figures. Zeros may or may not be significant, depending on their place in a number. When adding or subtracting the final result should have the same number of decimal places as the measurement with the fewest decimals. When multiplying or dividing the result should have no more significant digits than the factor having the fewest number of sig figs. When one force acts on an object, the object accelerates. When two forces act at the same time, the direction as well as the magnitude of the forces determine the motion of the object. If the forces are in the same directions, then the sum of the forces or net force will cause a larger acceleration. If two forces are in opposite directions, then the net force could be zero, which is also zero acceleration. A free-body diagram is used to show the relative size and direction of all forces acting on an object.
 * WHAT DO YOU THINK: **
 * WHAT DO YOU SEE: **
 * PHYSICS TALK SUMMARY: **

1) Newton's second law of motion states that acceleration is directly proportional to the force that acts upon the same object. Also, it is inversely proportional to the mass of the object. The acceleration and unbalanced force will act on the object in the same direction.  2) The acceleration will decrease 3) There is 30 newtons of force acting upon the object 4) Your weight would be higher than on earth, but your mass always stays the same
 * CHECKING UP QUESTIONS: **

1. "shaving ice" while stopping || -1500 N || 100 kg || **-15 m/s^2** || 3. 42 N / .30 kg = 140 m/s^2 4. 20 m/s^2 X .040 kg = .8 N  5a. A baseball is easier to throw than a bowling ball because of its weight and mass. The inertia of the bowling bowl is more because its mass is larger. 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. If you throw both with the same force the lighter one will still go farther, because the heavier one needs more force because its mass is bigger.  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. The force of your hand is still there, because the ball already left your hand and it is moving with your force.  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. 120^2- 50^2 = R^2= 130N, 67 degrees NE  14. 4000^2 + 5000^2 = R^2=  15. (F = m x a) F = (12.8 kg) (9.8 m/s^2); F = 125.44 N  16a. 40 N - 30 N = 10 N  16b. (a = f / m) a = 10 N / 5.6 kg; a = 1.8 m/s^2  17a. 30 N - 20 N = 10 N <span style="font-family: 'Times New Roman',Times,serif; margin-left: 0.25in;"> 17b. (a = f / m) a = 20 N / 100 kg; a = .2 m/s^2 <span style="font-family: 'Times New Roman',Times,serif; margin-left: 0.25in;"> 17c. If both net forces were pushing to the left then it would be 50 N. It would move at .5 m/s^2.
 * PHYSICS TO GO **
 * 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^ ||

1)125^2+125^2=R^2=177NE angle=tan-1(125/125)= 45 2a) 70-40= 30N south 2b) 30^2+40^2= 50N 2c) angle= tan-1(30/40)=37SE
 * PHYSICS PLUS p.169 **

A force is the energy or strength an object has behind it. The same amount of force will act differently because of the weights. Since a tennis ball is a lot lighter and bouncier the tennis ball with move faster. Since the bowling ball is heavier it will not go as fast as a tennis ball. You would need a lot more force, and also it does not rebound. The same amount of force can affect a tennis ball and bowling ball differently because they have different masses. It takes more force to move a bowling ball then a tennis ball.
 * WHAT DO YOU THINK NOW: **

** CHAPTER 2: SECTION 4 **
A girl standing on a stool holding a green apple and a red apple. The girl drops the red apple straight down and than throws the green apple over her friends hat. The apples are at the same vertical position and hit the floor at the same time. The momentum and force that the ball in the air is traveling with determine how far the object will go in the air. If the force is small than the ball will drop quicker and if the force is larger than the ball will be in the air longer. Also, any force that interrupts the balls movement in the air, because if there is wind, or an unbalances force than the ball can be forced the opposite way so it will drop quicker or it will be carried for a longer period of time if wind for example is blowing in the same direction.
 * WHAT DO YOU SEE: **
 * WHAT DO YOU THINK: **

1a) they hit the floor at about the same time. We can never be accurate to know if we are holding them at the exact same height, but they land in close range no matter what height. 2a) They hit at the same time 3a) The only thing the speed affects is the distance the ball with the greater speed went. It did not affect hitting the floor at the same time. 3b) yes it did the ball with the greater speed went a greater distance, but still hit the floor at the same time. 3c) 4a) They hit the floor at the same time. It takes the coin less time to get to the floor, but if the height is higher up the distance would be farther because there is more time for the coin to travel. When the height is lower there is not much time, so the distance is not that far. __** Part B: **__ 5a) I think that the ball will hit the person pushing the chair, or the ball will not be near the guy in the chair. 6a) The ball lands right back where it started. It lands right back above the chair so the kid in the chair is able to catch the ball in his hand. With the truck, the ball is thrown and the truck is moving, but the ball lands right back into the truck no matter what. The vertical compponent of velocity decreased on the way up, because it starts to slow down, on the way back down the vertical components get larger and larger, because it is than picking up speed because it had gravity pushing down on it. Horizontal components are unchanging. 6b) Speed, because the range will be bigger, meaning the path will be more spread out. Trajectory is path, resultants all strung together. __** Part C: **__ 1) As the horizontal launch velocity was increased so did the time in the air 2) As the horizontal launch velocity increased so did the range. 3) As the initial height was increases the time in the air was also increased 4) As the initial height was increased the range was increased 5) The initial speed and the height of the projectile 6) The initial speed and the height will affect the range of the projectile.
 * SECTION 4: INVESTIGATE **
 * __ Part A: __**

1+2) 4. People thought that the bullets would hit the ground at different times because one bullet travels horizontally as well as vertically and its going faster, but the shot bullet is going horizontal the other is going vertical. What they don’t know is that the vertical and horizontal velocity is equal. They may think this is different for the bullet, because the bullet is going faster and farther. 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. Also, with the chair and ball every single time the ball was thrown up, the kid in the chair could catch the ball, because it landed right in front of them.  7. The arrows will both hit the ground at the same time because they have to travel the same vertical distance. Even though the A is going at a greater speed because it is going horizontally its the same. 8. 3.6 km/h look at questions 1+2 on paper 9) 15 COS(37) = 11.9 m/s b) d=vit+1/2at^2 d=11.9(2.0)+ 1/2(0)(2.0)^2=23.8m 10) 12COS45=8.5m/s b) d=vit+1/2at^2 d= 8.5(.5)+ 1/2(0)(.5)^2 d= 4.24
 * PHYSICS TO GO: **


 * ACTIVE PHYSICS PLUS: **

Projectile is the only force is weight. They are launches through the air. (ignore air resistance). Trajectory is the path of a projectile. It is a parabolic shape. One type of launch is ground to ground a or a horizontal launch. Ground to ground are symmetrical around highest point. The y velocity is zero at the top, because it is still moving forward, but its constant speed. THe x and y information is independent from each-other. The acceleration on the y axis is always 9.8m/s^2 and because its going down its negative. The acceleration on the x axis is zero. If these two things are not true than it is not a projectile. Free fall force is only weight, but its 1 dimensional, so its only vertical, but the same as the y axis of the projectile. Take 10m/s away from each second when going up and add when you are going down but they will be negative.
 * PHYSICS TALK SUMMARY: **

1) Yes because acceleration is the same on both because they have the same distance to travel and the same velocity and acceleration, so they will land the same time 2) No it does not remain the same because it is gaining speed on the way down. 10m/s every second but it will be negative because it is going down. 3) the vertical velocity is 0 and the acceleration is -9.8
 * CHECKING UP QUESTIONS: **

The momentum and force that the ball in the air is traveling will determine how far the object will go in the air. If the force is small than the ball will drop quicker and if the force is larger than the ball will be in the air longer. Also, any force that interrupts the balls movement in the air, because if there is wind, or an unbalanced force than the ball can be forced the opposite way so it will drop quicker or it will be carried for a longer period of time, if wind for example is blowing in the same direction**.** Also, the angle of the launch will tell you how long the object will be in the air for.
 * WHAT DO YOU THINK NOW: **

CHAPTER 2: SECTION 5
There are four different people playing soccer and the first girl kicked the ball at a very steep angle, so that when the ball came down it came down straight on a kids head. Than that kid headed it at a smaller angle, so that it went into the et. Number 0 is trying to get to the ball but can not get their in time.
 * WHAT DO YOU SEE? **

If you launch something with a smaller angle, than the object will be in the air shorter and will not have that high of a max height. If you launch it at a steeper angle, than the longer the object will go in the air, but the smaller the x-component. If you use a greater launch speed when the angle is the same, than the farther the object will go because it has more force and speed behind it.
 * WHAT DO YOU THINK? **

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. Complementary angles have the same range, when you have a ground to ground launch. The greatest angle that has the greatest range is 45 degrees. After 45 than your range is going to get smaller and smaller, because you are spending more time in the air then involving your x component.
 * PHYSICS TALK SUMMARY **

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 in pairs are identical in all the parabolas.
 * CHECKING UP QUESTION **

1) 45 degrees creates the greatest range, because the velocity will be the same for both the y and x components. Any angle over this the object will be spending more time in the air than going a farther distance. 2a) If the launch angel is larger than 45 degrees, it will fall at the complementary angels range, which is closer to the object it was launched from compared to 45 degrees. 2b) If the launch angel is larger than 45 degrees, it will fall at the complementary angels range, which is also closer to the object it was launched from compared to 45 degrees. 3a) 60 degrees 3b) 75 degrees 4) They are probably not running fast enough. The x component is bigger than the y component so there for the angle has to be less than 45 degrees. 5) He was probably successful because he had the smallest possible mass and he ran very fast. If he is really good sprinter than he has a really fast x velocity and if he is good in high jump than he needs a y velocity, so therefore he will have a very high max height. 6a) The ball is not accelerating at point X 6b) The ball is not in motion at point X 7a) V= Vi +at (-9.8) (3) = 29.4 m/s Speed: 29.4 m/s 7b) 15 = Vi (1) 5 m/s 7c) d = Vi t d = 15 meters 8) The angle would have to be closest to 45 degrees to travel the greatest distance. 9) The biggest angle closest to 90 degrees 10a) The acceleration is downward. 10b) d = Vi t + 1/2 a t^2 -100 = -4.9 t^2 t = 4.5 seconds 10c) d = Vi t + 1/2 a t^2 d = 20 (4.5) d = 90 meters
 * PHYSICS TO GO **


 * ACTIVE PHYSICS PLUS **

If you launch something with a smaller angle, than the object will be in the air shorter and will not have that high of a max height. If you launch it at a steeper angle, than the longer the object will go in the air, but the smaller the x-component. If you use a greater launch speed when the angle is the same, than the farther the object will go because it has more force and speed behind it. 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.
 * WHAT DO YOU THINK NOW: **

** CHAPTER 2: SECTION 6 **
a kid in a chair is pushing off against a wall. In the first picture he is struggling to push away from it, because he was not moving and he was pushing the wall in. In the second picture he pushed off against the wall, the wall pushed him back so it was not a struggle to move away from the wall
 * WHAT DO YOU SEE: **

Bend your knees and push down and the force that you exert on the floor will make you jump. When your about to jump extend up and the force will transfer back over to you.
 * WHAT DO YOU THINK: **

Newtons third law of motion states that for every applied force, there is an equal and opposite force. The two forces always act on different objects. For example when you push on a wall, the wall will push you back away from the ball. Force always comes in equal and opposite pairs. The pairs act on different objects. They must be equal in size but point in a different direction. A diagram that shows the forces acting on an object is also called a free-body diagram. It is used to show the relative strength and the direction of all the forces acting on an object in a given situation. The arrow represents the direction the force is heading. The size of the arrow is the strength of the force.
 * PHYSICS TALK SUMMARY: **

1) Newton's third law of motion states that for every applied force, there is an equal and opposite force. The two forces always act on different objects. 2) Due to gravity earth pulls down a certain mass. Also, gravity is acting on the earth, because when object are pushing down on earth the earth is pushing at them. The same force is exerted but there are different accelerations because the earth is heavier. 3) A free body diagram illustrates the different forces acting upon an object. You can show these forces using vectors will arrows and labeling each force with a specific letter.
 * CHECKING UP QUESTIONS **

Physics To Go 1) Yes, due to Newton's third law it does. But it is going in the opposite direction (towards the hand) 2) The chairs are not intelligent, but the gravity of the earth pushes the same force that is being exerted on the chair, which in turn pushes up on us so that we do not fall and break the chair. 3) The scale measures the pressure that you put on the scale and a spring pushes back equal force, which than shows your weight. 4) When you hit a baseball the bat and the ball exert the same force on each other due to Newtons Third Law.The bat could break because the force the ball exerts could be a lot stronger than your swing or because both the force are so great that the bat cannot handle the pressure. 5) They will exert the same force, but because their masses are so different when the smaller of the two hit into each other the acceleration on the smaller guy will be greater, because less force is needed to damage him. 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. When the hockey player hits the boards the boards may push in but than exert the same force back on than because the boards do not move. 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. Also, padding causes lower acceleration which reduces force on hand 8a) 8b)
 * PHYSICS TO GO: **

ACTIVE PHYSICS PLUS:

You want to apply you force towards the floor and the force of the floor is going to exert the same force on you. Because you weigh less than the floor, the floor with accelerate you with the force and the floor will have the littlest acceleration. When you bend you knees and extend the force will make you go higher in your jump. The more force you apply by bending more the higher you will get.
 * WHAT DO YOU THINK NOW: **

CHAPTER 2: SECTION 7
You see two girls. On the ice she is pulling a shoe with a mouse in it and she is able to move the shoe easier. On the picture to the right the same girl is trying to move the shoe and the mouse on the sand, but it is harder because there is more friction which causes the force she needs to use to go up.
 * WHAT DO YOU SEE: **

Some sports require special shoes because in these sports you might need to cause more friction or less friction. For example in soccer you use cleats, because you are running on grass. You need to be able to run fast, so with the cleats the underneath of the shoe has spikes. These spikes stick into the grass causing friction and causes a force to push you back off the ground.
 * WHAT DO YOU THINK: **

µ coefficient of friction no units 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 only valid for a particular pair of surfaces
 * PHYSICS TALK SUMMARY: **

1. You can say they are equal to each other because the force that you are reading on the spring-scale is coming from the shoe sliding across a friction-filled surface. Also, because it is at constant speed. 2. It has no units because it is Newton divided by Newtons which cancel out each other in the end. 3. The coefficient of friction is determined by the force of friction over the normal force. This is called µ
 * CHECKING UP QUESTIONS: **

__**Part 1:**__ __**Table 1:**__
 * BOWLING WITH BLOCKS: **

__**Sample Calculations:**__
 * Tension (N) || Ff(N) || Total Weight (N) || µ || Class Average || %Difference ||
 * 3.5N || 3.5 || 11.7 || 0.3 || 0.332 || 9.64 ||
 * %difference=[.332-.30]/.332(100)=9.64%**

__**Part 2:**__ __**Table 2:**__

__**Sample Calculations:**__ ∑Fx=max -f=ma f=-ma
 * Mass (g) || Mass (kg) || Measured Time (s) || Measured Distance (m) || Ff(N) || Acceleration (m/s^2) || Calculated Vi(m/s) || Calculated time (s) || %error ||
 * 189.29 || 0.19 || 1.61 || 5.54 || 3.5 || -3 || 5.77 || 1.92 || 16.1 ||
 * 189.29 || 0.19 || 1.83 || 5.33 || 3.5 || -3 || 5.66 || 1.89 || 3.2 ||
 * 189.29 || 0.19 || 1.34 || 3.84 || 3.5 || -3 || 4.8 || 1.28 || 4.7 ||

∑Fy=may N=W

µ=F/N .30=0.19(a)/1.9

VF^2=Vi^2=2ad 0=Vi^2=2(-3.0)(5.54) Vi=5.77

1) During track a runner will want to increase friction between the floor and their shoes, so that they will run faster. To do this they can use spikes on their shoes, so that it increases friction. During conditions such as rain, the runner might need a different type of shoe to create more friction on the track, such as spikes too. 2) During ice-skating you want the least amount of friction, because you want to be able to glide across the ice. If there was a lot of friction the ice skater would not be able to get a lot of speed and would not be able to glide, they would get stuck. 3) The floors may be different at the other court, so she would need to know how slippery or rough the surface is before knowing if they are just right. 4) Tennis players should have shoes for the different surfaces so they can make sure that they have a good amount of friction no matter what type of court they are on. 5) ∑Fx = max N - w = 0  N = w  N = 600  µ = f/N  .03 = f/ 600  18 N = f
 * PHYSICS TO GO: **

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  The driver was lying because he said he was driving at 29 m/s when he was really going 32.3 m/s at the time

7) I think that they both remain the same, no matter how fast your going, because than it would be different for everyone even if they were standing right next to each other than. 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 faster the track runner can accelerate. This makes you go faster, because when wearing spikes the spikes stick into the ground so you can push off instead of sliding. 10) Friction is very important when you run because it keeps you from sliding. Cleats are used because it causes more friction when you run, so that you wont slip and fall.

**ACTIVE PHYSICS PLUS:**



**WHAT DO YOU THINK NOW:** Some sports require special shoes because in these sports you might need to cause more friction or less friction. For example in soccer you use cleats, because you are running on grass. You need to be able to run fast, so with the cleats the underneath of the shoe has spikes. These spikes stick into the grass causing friction and causes a force to push you back off the ground. Also, when running track you need to cause more friction so you wear spikes. In different conditions such as rain and depending on the type of surface you are on there will be different shoes to cause more friction. When bowling you also wear shoes that make you not slip, because if you bowl with regular shoes on you may slip because the surface is slippery.

** CHAPTER 2: SECTION 8 **
In the picture there are three pole vaulters, which are each running at different speeds, and jumping from different distances. There is one that is going up really high and that others are either jumping off the ground or not even in the air yet. This is not possible, because once you want to try and clear higher heights, the longer the pole needs to be and the more bendy it needs to be. If you try to jump over a 12 m high bar with an 11 m pole, you might not make it over because the pole will sink down because your weight is also weighing down on the pole. The weight, the height of the pole, the deflection of the pole, and the speed you are going, and the form that you are jumping with.
 * WHAT DO YOU SEE: **
 * WHAT DO YOU THINK: **

__Prelab Activity:__ a) to blast the penny high in the air I held one end of the ruler off the table and the other end on the table. Than i put the penny on the side off the table and held it down and than let go and the penny flew up. b) If you put the ruler more off of the table and press it the higher it goes up. If you place the ruler a little off the table you need a bigger deflection for the penny to go higher up. If you place the ruler half of the table and half on than you will get the most power. Also the position of the penny on the ruler makes a difference, because if the penny is by the end of the ruler than it will go higher, than if the penny was placed closer to the table. Also, the mass will affect how high it goes, because if the mass if heavier and you deflect it the same amount as you do with a lighter penny, the heights will differ. 1a) I will be able to conclude how the deflection of the ruler alters the height of the penny. 1b) I will record how big the deflection is and than I will record the height of the penny when it is let off the ruler. 1c) A ruler, penny, and a meter stick 1d) I will analyze my data by keeping a chart comparing the deflection to the height that the deflection makes the penny go in the air. Than I will look over my data and see how each different measured deflection affects the height. POSTER IS IN CLASS!
 * INVESTIGATE: SECTION 8: **

K=spring force constant x=the stretched or compressed distance || The law of conservation of energy - Total energy remains constant but the types of energy can change. penny pushing down on ruler=work when it is in the position= elastic
 * PHYSICS TALK SUMMARY: **
 * Type of Energy || Description || Equation ||
 * Kinetic Energy || Energy possessed by an object when it is moving || KE=1/2 m v2 ||
 * Gravitational Potential Energy || Energy possessed by an object when it is above its lowest point || GPE=mgh ||
 * Elastic Potential Energy || Energy possessed by a spring when stretched or compressed || EPE=1/2 k x2
 * Work || caused by a force acting over some distance parallel to the direction of motion. Not really energy, but creates energy |||| W=F*d ||

1.) For the energy of an object to change a force needs to be acting on the object. 2.) The penny being launched gets its energy from the ruler it is launched from, because the rule has elastic potential energy. This is acting as a spring on the penny 3.) The vaulter needs to get a running start at first which will give him kinetic energy which is needed for him to get over the bar. Than he also needs elastic potential energy, which he gets from the pole as he is flying in the air while the pole is bending. When the pole unbends it will shot the vaulter up. Then he needs potential energy as the pole straightens. Lastly as his height changes, he needs gravitational potential energy to launch him vertically upwards so he will get over the pole 4.) The units of all of these energies is Joules.
 * CHECKING UP QUESTIONS: **

1) work in to kinetic to gravitational potential energy= kinetic energy to work out. 2) EPE to Kinetic to Work on the ball to gravitational 3) kinetic to potential 1/2mv^2=mgh 7.3m 4) Because you need to know the force, and the speed that the vaulter is running at 5) If the poles heat up they are more capable of bending. If the temperature increases than your height will 6) She would need to be going very fast in a very short amount of time to go up that high 1/2v^2=9.8(4.55) 9.44m/s 7)He would have ran faster than her because of the difference in height Emmas: 1/2 mv^2= mgh 1/2 v^2= (9.8) (4.55) v=9.44 m/s Sergei's: KE=GPE 1/2v^2=gh 1/2 v^2= (9.8)(6.14) v=10.97 m/s 8a) GPE (mgh)= W = KE= 1960 J KE= 1/2 mv^2 1960= 1/2 (2)v^2 v=44.3 m/s 8b) yes because the mass cancels out on both sides 9) k=1500n/m x= 25 cm w=? W=EPE W=1/2kx^2 =1/2(1500)(0.25) =47J 9b) m=0.1kg v=? EPE=KE 1/2kx^2=-1/2mv^2 47J=1/2(0.1)v^2 31m/s=v 10) k=315n/m x=0.30m 10a) w=? F=47.3N W=EPE W=1/2kx^2 =14.2J 10b) F=? if d=0.30m Fd=1/2kx^2 F(0.3)=14.2J F=47.3J 11) GPE=EPE mgh=1/2kx^2 (0.04)(9.8)(1)=1/2(18)(x^2) x=0.21m 12a) F=ma N=Kg*m/s^2 12b) W=fd J=nm 12c) GPE=mgh =(kg*m/s^2)*m =n*m =J 12d) KE= 1/2 mv^2 13) EPE --> KE --> GPE --> KE 14) KE = W = GPE 15) The pitcher throws the ball towards the player, the ball obtains kinetic energy. The player winds up and swings the bat which comes in contact with the ball. The ball goes up, up, and up into the air. It has kinetic energy going up. Once it reaches its highest point, the ball has Gravitational Potential Energy with a velocity of zero, because the ball is up in the air. As the ball is on its way back down to the field there is kinetic energy which it is actually loosing on the way down. After hitting the ground the ground does work, which stops the ball. 16)
 * PHYSICS TO GO: **

This is not possible, because the heat that is made throughout this process is released so that your max height is decreased. IT first start out with work put in than kinetic energy than potential energy, than to kinetic energy and work out. The kinetic energies have to be equal throughout this process for this to happen, and they aren't. Also, for the speed that the vaulter will be running and the force that they are acting on the pole with will make the pole bend to much and the person will just sink down instead of going higher, because it bend more.
 * WHAT DO YOU THINK NOW: **

** CHAPTER 2: SECTION 9 **
I see a figure skater who is turning up in the air, and than i see a helicopter who is as high as the figure skater. If the same 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 the same amount of time as someone who is just jumping. They are using more force so they will go higher, faster and stay in the air longer.
 * WHAT DO YOU SEE: **
 * WHAT DO YOU THINK NOW: **

The work that you do when jumping is equal to the product of the applied force and the distance. When you are in the ready position of a jump you have elastic potential energy which is when a spring is acting on you. The energy of you three positions in a jump must be equal. There is also sound energy, light energy, chemical energy, electrical energy, nuclear energy, and the internal energy that shows itself through temperature. The total of all energies at any one time must equal the total of all energies at any other time. In all of these examples the sum of all the energies at each position is equal to sum of all the other energies in each position.
 * PHYSICS TALK SUMMARY: **

1) It energy comes from elastic potential energy that is causes when you are bending your knees. The energy comes from the chemicals reacting in your muscles. 2) In the launch position and at the peak of your jump, the person will have gravitational potential energy, because they are already in the air. Also you have kinetic energy because you are moving your knees to bend. As they are jumping up though there will be kinetic energy, because they are not at rest anymore. This will turn into gravitational potential energy. 3) Nuclear energy, sound energy, and light energy are all different types. They are energies that show through temperature.
 * CHECKING UP QUESTIONS: **

INVESTIGATE SECTION 9: 1) W=GPE Fd=mgh 2a) The force exerted the floor and back at you 2b) We will record the height. weight/mass, and distance from my hips to the floor 2c) Meter stick 2d) By comparing the different trials and than solving the equation and finding out the force. Than we will use a scale and actual measure the force. Calculations: Fd=mgh F(.21m)=48.9(9.8)(.46) F=1102.2



My force when I used the platform was 1753.12N. This was a lot higher than the one that I calculated myself, because when I estimated my weight it was off, so that changed my results. Also, when I jumped on the platform it might not of been the same measurements that I had measured during my trials. Every jump you do is going to be different, so that is why my force was difference in the two calculations.

1) W= GPE FD= mgh W=50 (9.8)(1) W= 490 J 2) W + GPE -> Kinetic energy -> Work 3) In order to test to see if this is correct we could watch the video like we did with the others and mark where the basketball players hips are at each time interval. We than would conclude that there is a parabola so there is no such thing as hanging there. 4) Although it may seem like the laws of gravity can be defied when doing sports like ice skating, it is not true. The person might have evidence that seems to be true but it is not, because we all see things differently. Their small displacement might help persuade the person that the law of physics is defied, but based on real proof and evidence they are not. 5) A person can increase their vertical jump by bending their knees farther down which increases their elastic potential energy and by decreasing their mass without loosing their muscle, because with more muscle they can add more force when jumping 6a)W=FD W=1(1)= 1 J 6b) W=FD W= 1 (10)= 10 J 6c) W= 10 (1) W= 10 J 6d) W= FD W= .10 (100) W= 10 J 6e) W=FD W= 100 (.10) 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 W= (50) (43) W= 2150 J 10) KE= 1/2mv^2 KE= 1/2 62(8.2)^2 KE= 2084 J 11a) a= f/m a= 30/5 a= 6 m/s^2 11b) W=Fd W=30 (18.75) W= 563 J 12a)W= FD 40,000=3200 N (d) D= 12.5 meters 12b) a=f/m a= 3200/1200 a= 2.7 m/s^2 13) KE--> W KE= W 1/2 mv^2= FD 1/2 (.150) (40)^2= W 120 J= W 14) W= KE FD= 1/2 mv^2 417d= 1/2 (64) (15)^2 417d=7200 d=17.27 meters 15)
 * PHYSICS TO GO: **

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">16) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">17) 18)The volleyball player is running towards the net to spike the ball. She runs at her fastest speed, using kinetic energy. Than she jumps into the air with her arms up forming a parabola like shape while going up in the air till the time she lands on the ground. Because of her cheetah like speed, her kinetic energy was much higher so she was able to get rather high off the ground. At her highest point she has gravitational potential energy because she is off the ground and in the air. When she comes in contact with the ball she starts to come down to the ground loosing her kinetic energy as she hits the ground.
 * || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">KE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">GPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">EPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Sum ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Running || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Full Bend of pole || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">10 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">90 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Peak Height || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Landing || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">40 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">60 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">100 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Cushion Collapse || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 ||
 * || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">KE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">GPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">EPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Sum ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Peak Height || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1000 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1,000 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Landing || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">150 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">350 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">500 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1,000 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Lowest height || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1,000 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1,000 J ||
 * || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">KE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">GPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">EPE || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Sum ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Top of Mountain || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">900 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">900 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Middle of Mountain || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">450 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">450 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">900 J ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Bottom of Mountain || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">900 J || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">0 || <span style="font-family: Arial,Helvetica,sans-serif;">900 J ||

<span style="font-family: Arial,Helvetica,sans-serif;">1a) GPEi=KEf+ GPEf <span style="font-family: Arial,Helvetica,sans-serif;"> mgh=1/2mv2+mgh <span style="font-family: Arial,Helvetica,sans-serif;"> (9.8)(50)=1/2v2+(9.8)(30) <span style="font-family: Arial,Helvetica,sans-serif;"> vf=19.8m/s
 * ACTIVE PHYSICS PLUS: **

<span style="font-family: Arial,Helvetica,sans-serif;">2) GPEi+EPEi=KEf­ <span style="font-family: Arial,Helvetica,sans-serif;"> mgh+1/2kxi2=1/2mvf2 <span style="font-family: Arial,Helvetica,sans-serif;"> .300(9.8)(2)+1/2(60)(.40)2=1/2(.300)v2 <span style="font-family: Arial,Helvetica,sans-serif;"> v=8.4 m/s

<span style="font-family: Arial,Helvetica,sans-serif;">3)

WHAT DO YOU THINK NOW: