Chapter 2 - Question Keys - SFSU Physics & Astronomyjfielder/Chapter2TestSolns.pdfPET Chapter 2 Question Keys 2 2. In the left column below there are three situations where a cart

Chapter 2 - Question Keys

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 four sections (A,B,C,D).

During each of the four separate periods shown on the graph (A, B, C, D), was an unbalanced force acting on the cart? YES or NO. If not, how can you tell from the graph? If yes, did the unbalanced 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 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.

B 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.

C The speed of the cart is constant. For this to happen the forces acting on it must be

balanced. D The speed of the cart is decreasing again. For this to happen the forces must be

unbalanced, with the strongest force in the opposite direction to the motion.

PET Chapter 2 Question Keys 2

2. In the left column below there are three situations where a cart is acting on by more than one force. The direction and strength of each force is shown. In the second column state whether the forces acting on that cart are balanced or unbalanced. If balanced, leave the third column blank. If unbalanced, in the third column draw the net force on the cart (the single equivalent force) and make sure you include its direction and strength in N.

Object with forces acting on it Are forces

balanced or unbalanced?

If unbalanced, draw the net force

(a)

Unbalanced

7 N

(b)

Balanced

(c)

Unbalanced

8 N


3. 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

10 N

b) 50 N

40 N

25 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. 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.)


4. 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. 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.

6. 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 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.


7. 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.

Fan #2

Fans 1&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.)


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 speed-time 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 oncart by Fan #1

Force exerted oncart by Fan #2


8. 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.)


9. A group of students arrange

two level tracks side-by-side so they can have a race between two carts. They mount identical fan units (each with two real batteries) on two identical carts. When the two carts, with fans turned on, are released

simultaneously from the end of the tracks they speed up at the same rate, traveling side-by-side, and so the race ends in a tie (Experiment 1). The students then add extra mass to one of the carts and repeat the experiment (using the same fan units), and record speed-time data for both carts (Experiment 2).

a) The next week, when they look at the speed-time data they graphed

(shown below), there are two lines (labeled A and B), and they are not sure which is which. Can you help by identifying which line represents the motion of the cart with the added mass? Justify your choice.

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Time (s)

Spee

d (c

m/s

) A

B

Line B represents the motion of the cart with added mass. Since the fan units were identical they would have provided the same strength force on each cart. However, the cart with the added mass would have sped-up at a slower rate than the one without the extra mass. The line that represents a lower rate of speeding up is B.


b) However, one of the students remembers that they also attempted to break the tie in Experiment 1 by adding a additional battery to one of the fan units without adding extra mass to either cart (Experiment 3). Could the speed-time data shown in the graph on the previous page be from Experiment 3? Yes or No. Justify your answer.

Yes, the data could be from Experiment 3. In this experiment two different strength forces were applied to identical carts. This would mean that the cart with the stronger fan force acting on it would speed up at a higher rate than the other cart – this would correspond to line A, with line B being the cart with the weaker fan force acting on it.

10. A cart has a fan unit and a friction pad

attached. A student adjusts the friction pad so it rubs lightly against the table. When the fan is turned on, the cart speeds up slowly to the right.

Explain why the cart speeds up to the right.

Draw the Force Diagram:

Write the explanation:

For an object to speed up an unbalanced force (or unbalanced combination of forces) must act on it. For the cart to speed up slowly to the right the forces acting on it must be unbalanced, with the strongest force pushing to the right. This must mean that the force exerted on the cart by the fan must be stronger than the frictional force opposing the motion. (However, it cannot be very much stronger, since the slow rate of increasing speed indicates that the net force is not very large.)

Force exerted on cart by fan unit Frictional force exerted

on cart by track


11. A group of students arrange two level tracks side-by-side so they can have a race between two carts. They mount identical fan units (each with two real batteries) on two identical carts. When the two carts, with fans turned on, are released

simultaneously from the end of the tracks they speed up at the same rate, traveling side-by-side, and so the race ends in a tie. The students then add some extra mass to one of the carts (Cart A) and add an extra battery to the other cart (Cart B). They then repeat the race and see that Cart B now speeds up more quickly than Cart A and so pulls ahead of it and wins the race. Your task is to write an explanation for why Cart B now speeds up more quickly than Cart A

Explanation: Why does Cart B speed up more quickly than Cart A?

Draw the Force Diagrams:(One for each cart)

Force of fanunit on cart

Cart A: Added mass and

2 batteries in fan unit

Force of fanunit on cart

Cart B: No added mass and

3 batteries in fan unit Write the explanation: Cart B has two factors that make it speed up more rapidly than Cart A. First it has less

mass and so, even with an equal force, it would speed up more quickly. Second it has a stronger force (due to the extra battery) so this would make it speed up more quickly also, even if the masses were the same. Both factors work in favor of Cart B so it speeds up a lot more quickly than Cart A.


12. A small child is pushing the box of toys across the room at a constant speed.

Create an explanation for why the box moves at a constant speed as the child pushes it.

Draw the Force Diagram:

Write the explanation:

For an object in motion to move at a constant speed the forces acting on it must be balanced. If the box in question does move at a constant speed this must mean that the strength of the force acting in the direction of motion must be exactly equal to that of the force opposing its motion. Therefore the box moves at a constant speed because the strength of the child’s push is equal to that of the frictional force exerted on it by the floor.

Force exerted on box by child

Frictional force exerted on box by floor

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Chapter 2 - Question Keys - SFSU Physics & Astronomyjfielder/Chapter2TestSolns.pdfPET Chapter 2 Question Keys 2 2. In the left column below there are three situations where a cart