Practice TEST. A The cart is at rest (constant speed of zero). The forces acting on it must be balanced for it to remain at rest.

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1 Practice TEST 1. Shown below is a speed-time graph for a cart moving in front of the motion sensor. For convenience it has been divided into five sections (A,B,C,D,E). B C D A E During each of the five separate periods shown on the graph (A, B, C, D, E), was the combination of forces acting on the cart balanced or unbalanced? If unbalanced, did the strongest force act in the same direction as the cart s motion, or against it. Briefly explain how you can tell this from the graph? A The cart is at rest (constant speed of zero). The forces acting on it must be balanced for it to remain at rest. B The speed of the cart is increasing. For this to happen the forces must be unbalanced, with the strongest force in the same direction as the motion. C The speed of the cart is decreasing. For this to happen the forces must be unbalanced, with the strongest force in the opposite direction to the motion. D The speed of the cart is still decreasing. For this to happen the forces must be unbalanced, with the strongest force in the opposite direction to the motion. E The cart has stopped and is at rest (constant speed of zero). The forces acting on it must be balanced for it to remain at rest

2 2. Two students were discussing if they could tell whether a force (or an unbalanced combination of forces) was acting on an object just from observing its motion. If an object is moving in any manner whatsoever then there must be a force acting on it in the direction of motion to keep it moving. If no force acted to keep it moving it would simply stop. I disagree; it depends what the motion is like. Just because an object is moving there does not necessarily have to be a force acting on it. Daryl Luisa Which student do you agree with (if either), and why? I agree with Luisa. She has an idea consistent with those we developed in class. The effect of a force (or an unbalanced combination of forces) acting on a moving object is to change its motion in some way, either making it speed up, slow down, or change direction. If the motion of an object is not changing in any way this means that no force (or a balanced combination of forces) is acting on it. So, just because an object is moving does not necessarily mean a force is acting on it. Daryl s idea is not consistent with those we developed in class. He says that if no force acts an object will stop, but we saw that objects stop because a force does act on them (in a direction opposite to their motion). 2

3 I agree with Victor. He has an idea that is consistent with those we developed in class; that objects slow and stop because a force (or unbalanced combination of forces) acts on them in a direction opposite to their motion. Kristen s idea is not consistent with our class ideas. She seems to be saying that there is still a force pushing the car forward after the initial shove, but our idea was that the force of the shove is gone as soon as the hand loses contact. Her idea that the car slows down because the forward force gets weaker is also inconsistent with our class ideas. We said objects slow down because stop because a force (or unbalanced combination of forces) on them in a direction opposite to their motion. Daryl s idea might be OK, but without more information it is impossible to tell. He implies that for the car to keep moving a force is needed in the direction of motion. If he is accounting for the effects of the friction force that slows the car down, he is correct, but he doesn t say that. On the other hand his thinking could be something like Kristen s, in that he thinks that for any motion to continue a continuous forward force is needed, even in the absence of friction, and without such a forward force it is just natural for the car to stop. This is not consistent with our class ideas. Samantha thinks that if balanced forces act on a moving object, then it will slow and stop. However, in class we found out that when balanced forces act on an object its speed will remain constant. So if balanced forces acted on the car after the initial shove then it would not slow down, but continue at a constant speed. 3. A soccer player kicks a ball into the net. When the soccer ball hits the net, it slows to a stop. Below, is a force diagram a student drew to describe the forces acting on the ball as it slowed down. Is this force diagram complete or is there something missing and/or incorrect? If complete and correct, justify your answer by writing a couple of sentences. If there is one or more things missing or incorrect, re-draw the diagram so it is fully correct, and justify your diagram by writing a couple of sentences. 3

4 I think the force diagram is incorrect. The picture shows the ball in the air as it hits the net, not rolling across the ground, so there will be no frictional force of the ground on the ball. Instead, the force that opposes the motion of the ball to slow it down comes from its interaction with the net. I would redraw the diagram like this: Force of net on ball 4. Five identical crates are initially at rest, side-by-side. One is acted on by a single force of 45 N, as shown. 45 N Which of the other crates, shown below, would move side-by-side with the crate described above? (Choose as many as you think appropriate.) a) 25 N 10 N b) 50 N 25 N 10 N 40 N 20 N c) 75 N 30 N d) 15 N 60 N Briefly explain your choice(s). Since they are identical, in order for the other crates to move side-by-side with the first one they will need to have a net force acting on them that has the same strength and direction as the single force acting on the first crate; namely 45 N to the right. 4

5 Both of crates b) and c) have this. Crate b) has a total of 90 N to the right and 45 N to the left. Subtracting 45 N from 90 N gives a net force of 45 N to the right. Crate c) has 75 N to the right and 30 N to the left. Subtracting 30 N from 75 N gives a net force of 45 N to the right. (The net force on crate a) is only 25 N to the right. The net force on crate d) is 45 N to the left.) 5. Block A, shown below, is moving to the right. At the moment shown, three different forces are acting on the block. The strengths and directions of the three forces are shown in the force diagram. a) Will block A speed up, slow down, or move at constant speed? Briefly explain how you know. Block A will slow down as it moves. This is because the forces acting on it are unbalanced, with the net force acting opposite the motion of the block. b) Suppose there was another block (B) that was identical in size and mass to block A. At the same moment shown above, block B is alongside block A and is moving at the same speed as block A. What single force should be applied to block B, so it continues to move side-by-side with block A? Draw this force (strength and direction) on the block below, and briefly explain how you know. 3 N Since the blocks are identical, Block B will need the same net force acting on it in order to move side-by-side with Block A. The net force acting on Block A is 3 N to the left (12 N to the left minus a total of 9 N to the right) so that is the single force that should act on Block B. 5

6 6. A hockey player uses his stick to maintain a continuous constant strength push on the puck as he moves it across the smooth ice. Assuming that the effects of friction are negligible, which of the following choices best describes the motion of the puck while this constant strength push is acting on it? a) The speed of the puck will continuously decrease. b) The puck will move at a constant speed. c) The speed of the puck will continuously increase. d) Something else you describe it. Briefly explain the reasoning behind your choice (remember to include a description of the motion if you chose option d). We learned in class that when a constant strength force acts on an object, it speeds up. As long as the force continues to act the puck s speed will continuously increase. 7. A large block is on rollers so that it can move across a level surface as if there was no friction affecting it. After they have started the block moving to the right, two men want it to continue moving in the same direction, at a constant speed. Below are force diagrams representing four possible arrangements of forces the men could apply to the block. The situations are also described briefly in words. A. Pull to the right is stronger than the pull to the left. B. No-one pulls, either to the right or the left. C. Pulls to the right and the left are of equal strength. D. Only one person pulls to the right. No-one pulls to the left. 6

7 a) Indicate all the situations shown above (if any) that you think would result in the block moving to the right at a constant speed after it has already started moving. Briefly explain the reasoning behind your choices. The diagrams all show the block moving to the right. Since it is already in motion any unbalanced combination of forces would result in a change in speed. Only a balanced combination of forces would result in motion at a constant speed. So C would work. B would also work since having no forces act is the same as having a balanced combination of forces. b) For those situations that you did not select in part a), what do you think the motion of the cart would be like? Again, explain your reasoning. In both A and D a stronger force acts in the direction of motion than acts against it. In this case both situations would result in a steadily increasing speed. 8. A small child attempts to push a box full of toys across the floor in his playroom. However, despite pushing as hard as he can, the box does not move. Which one of the following statements best describes the reason the box does not move while he is pushing it. a) The force resisting moving the box is greater in strength than the child s push. b) The child weighs less than the box does. c) The force resisting moving the box is equal in strength to the child s push. d) The strength of the child s push is greater than the strength of the force resisting moving the box, but not great enough to move it. Please explain your reasoning If an object is at rest and remains at rest, then the forces acting on it must be balanced. This means the force of the boy and the force resisting him must be equal. (Note: If a) were true the box would start to move in the opposite direction to the child s push!) 7

8 9. The child in the previous question calls for help and his mother comes and helps him push the box, in the same direction. Which one of the following statements best describes why the box now begins to move. a) The combined push of the mother and child is equal in strength to the force resisting the movement of the box. b) The mother weighs more than the box does. c) The combined push of the mother and child is greater in strength than the force resisting the movement of the box. d) The strength of the mother s push alone is greater in strength than the force resisting the movement of the box. Please explain your reasoning For an object at rest to start moving, the forces acting on it must be unbalanced. This means the combined forces of the boy and the mother must be greater than the force resisting them. 10. A ball moves in a curved path inside of a curved tube. The picture to the right shows the ball inside the tube at three different times (times 1, 2 and 3). The arrows represent the speed of the ball at those three times. At time 2 is there an unbalanced force acting on the ball? If yes, add an arrow to the picture to show the approximate direction of Unbalanced force the unbalanced force, and briefly justify your answer. If no, explain why not. Yes, there is an unbalanced force acting on the ball. We know this because as it is moving through the curved tube it is changing direction, for which a sideways unbalanced force is needed. This force would need to be pointed toward the inside of the curved path, as shown on the figure, in order for the ball to follow the path (which is part of a circle). 11. A soccer ball is rolling across the ground. A child briefly taps the ball with her foot at right angles to its direction of motion. A force diagram for the interval 8

9 of time that the child s foot is in contact with the ball is show below to the left (top view). During Tap After Tap In the picture to the right, draw a motion arrow showing how the ball will be moving after the tap. Pay attention to both the length and direction of the motion arrow. Briefly explain why you drew it this way. The sideways tap will not change the speed of the ball, only its direction, so the length of the motion arrow will be the same but it will point in a different direction. Since the ball was already moving to the left it will continue to do so (since no force acted to make that change), but it will also move upward at the same time, due to the effect of the tap. The combination of these means that the ball will be moving diagonally up and to the left after the tap. 12. After being given a quick push, a small ball moves at a constant speed inside a flat circular track. (A top view is shown to the right.) A section of the track is missing, as shown, and the ball leaves the track and rolls across the table top. Which line in the diagram best represents the path the car will follow when it leaves the track? Briefly explain the reasoning behind your choice. C D B A Line B best represents the path of the ball when it leaves the track. The track is supplying the sideways force that points toward the center of the circle and keeps the ball moving in a circle. When that force is removed (at the end of the track) there is no longer a sideways force to change the direction of the ball so it now moves in a straight line in the direction it was headed at the instant it left the track. 9

10 13. Imagine you had two different fan units. Fan #1 had more batteries than fan #2. Fan #1 can push the cart with a force of 20 N. Fan #2 can push with a force of 5 N. Suppose you start an experiment by mounting Fan #1on a cart and release the cart from rest on a very smooth track. You can ignore the effects of friction throughout this problem. Below is a speed time graph for the motion of fan #1 pushing the cart. Fans 1&2 Fan #2 a) Suppose you replaced fan #1 with fan #2 (the weaker one) and mounted it by itself on the same cart. When the cart is released from rest, you observe that it speeds up. Sketch what the speed-time graph for Fan #2 might look like on the graph above. Label it Fan #2. Below, briefly explain why you drew the graph the way that you did. Fan #2 is a lot weaker than Fan #1 so the cart will speed up at a much slower rate with Fan #2 than it did with Fan #1. (In fact, since friction can be ignored, and since the force is only one fourth a strong, the cart will speed up at one fourth the rate, so it will only reach a speed of about 20 cm/s after 2.5 seconds, as opposed to about 80 cm/s with Fan #1.) 10

11 b) Now suppose you mount both fans on the same cart, but with the two fans trying to push the cart in opposite directions. When you release this cart from rest you observe that it speeds up. Sketch what the speedtime graph for the combined fans might look like on the same graph on the previous page. Label it Fans #1 & #2. Below, briefly explain why you drew the graph the way that you did. With both fans mounted on the cart in the way indicated there will be an unbalanced combination of forces acting on it. The strength of the net force will be 15 N (20 N in one direction, minus 5 N in the other direction). This net force will make the cart speed up at a rate that is slightly lower than that for the 20 N force alone. (The extra mass of the added fan will also be a factor in reducing the rate of speeding up.) c) Below, draw a force diagram for the cart with the two fan units on it while the cart is speeding up. (Remember to include all relevant forces, label them appropriately, and also include a speed arrow if appropriate.) 20 N 5 N Force exerted on cart by Fan #1 Force exerted on cart by Fan #2 11

12 14. A group of students arrange two level tracks side-by-side so they can have a race between two carts with fans mounted on them. They start with the two fan units having the same strength (same number of batteries). Cart #2 has extra blocks on it so its mass is greater than the mass of cart #1. The students next want to adjust the strength of fan unit #1 (by changing the number and size of batteries) so the two carts will tie in a race (that is, when turned on and released they will each speed up at the same rate). Should the strength of fan unit #1 be made greater than, equal to, or less than the strength of fan unit #2? The strength of fan #1 should be made less than the strength of fan #2 Justify your answer. Since cart #1 has less mass than cart #2 it will require less force strength to make it speed up at the same rate. (We learned in class that the more mass an object has the slower its rate of speeding up will be for a given force strength.) 12