Runaway Boards: Testing Stoppers for a Skate Park Walkway

Use Newton's third law and test data to choose a stopper for loose skateboards.

Testing the stoppers

Read the passage and study Table 1. Then answer the questions.

Boards on the Loose

1At Wexley Park's skate park, the bowl and the banks are busy every afternoon. When a skater falls, the board often keeps rolling. Runaway boards shoot off the bottom of the long bank, across the flat and into the walkway where parents and younger kids stand to watch. Last summer one hit a parent's ankle hard enough to leave a deep bruise. The parks department asked the eighth-grade physics club at Ashby Middle School to test board stoppers that could be bolted along the edge of the walkway before the busy summer season begins.

2The club started with Newton's third law. When two objects collide, each one pushes on the other. The two forces are the same size, point in opposite directions and act at the same moment. This is true even when only one object was moving before the collision or when one object is far heavier than the other. The law works for pushes without a crash, too: when a skater pushes off, her foot pushes back on the ground, and the ground pushes her foot forward just as hard.

3To test each stopper, club members Nilufar Okoro and Kenji Szilagyi let a 2.0 kg skateboard roll down a test ramp so it reached 4.0 m/s at the bottom and hit the stopper head-on. A force sensor taped to the board's nose recorded the peak push of the stopper on the board, and a video app measured the board's speed after the hit. They ran each test three times with the same board, ramp and starting point, and Table 1 shows the averages. Each stopper was bolted to a concrete floor, as it would be at the park.

4The parks department gave four criteria. First, the board must not get past the stopper. Second, the board bounces back at no more than 1.0 m/s, so it does not roll fast back into the skating area. Third, the peak force between the board and the stopper is no more than 1,500 N, because the bolts that hold a stopper to the concrete can work loose above that. Fourth, the stopper is no taller than 10 cm, so people can step over it without tripping.

Table 1. 2.0 kg board hits each stopper at 4.0 m/s (averages of three trials)
Stopper	Height (cm)	Board got past?	Peak force on board (N)	Bounce-back (m/s)
A. Concrete curb	10	No	2400	2.2
B. Hard rubber strip	8	No	1100	1.4
C. Foam-core rubber bumper	8	No	600	0.6
D. Stiff brush strip	6	Yes, at 1.5 m/s	150	—
E. Thick foam pad	15	No	400	0.4

The sensor measured only the push of each stopper on the board. Use Table 1 and paragraph 2.

How large was the peak push of the board on Stopper B? N

Think about the moment of peak force when the board hit the concrete curb (Stopper A). Which statement about the forces is correct?

A. Each pushed the other with 2,400 N: the curb toward the ramp, the board away from it.
B. The curb pushed back on the board after the board had stopped pushing on the curb.
C. The board pushed the curb with more than 2,400 N, since the board was the moving object.
D. The board pushed the curb with 2,400 N, and the curb pushed back with less, since it did not move.

The board hit the concrete curb at 4.0 m/s and bounced straight back at 2.2 m/s. Count the reversal as part of the change: going from 4.0 m/s forward to a stop is a change of 4.0 m/s, and speeding up backward adds more.

By how much did the board's velocity change during the hit? m/s

The board's velocity changed by 4.6 m/s with the foam-core bumper (C), not much less than with the curb, yet the peak force was only one quarter as large. Which explanation fits the data best?

A. The bumper added its mass to the board, so the board hit it more slowly.
B. The bumper squashed, so the board's velocity changed over a longer time.
C. The bumper is lighter than concrete, so it pushed back less than it was pushed.
D. The board pushed less on the bumper than the bumper pushed on the board.

In test A, the board's motion changed a lot, but the curb did not move at all that anyone could see. Which explanation fits Newton's third law?

A. The curb pushed on the board harder than the board pushed on the curb.
B. The curb pushed on the board, but the board's push on the curb was too small to count.
C. The curb is bolted to the floor and Earth, so the same push barely changes their motion.
D. The curb felt no force from the board, because concrete is harder than a skateboard.

Choosing a stopper

Use Table 1 and the four criteria in paragraph 4.

Sort each stopper by how it does on the four criteria. Each stopper fits one group.

A. Concrete curbB. Hard rubber stripC. Foam-core rubber bumperD. Stiff brush stripE. Thick foam pad

Meets all four criteria	Fails the bounce-back or force limit	Fails the stopping or height rule

The thick foam pad (E) gave the slowest bounce-back of all the stoppers that stopped the board. Why should the parks department still not choose it?

A. Its peak force of 400 N is above the limit the bolts can hold.
B. It is 15 cm tall, so people in the walkway could trip on it.
C. The board got past it, because the thick foam was too soft.
D. Its bounce-back of 0.4 m/s is faster than the 1.0 m/s limit.

When a runaway board hits a skater

Read the situation, then answer the questions.

On the flat, a 2.0 kg runaway board rolls into Delphine, who is standing still on her own skateboard. Delphine and her board together have a mass of 50 kg, and both can roll freely. During the hit, the runaway board's velocity changes by 5.0 m/s. The two push on each other with equal forces for the same short time, so an object with 25 times the mass has its velocity change only 1/25 as much.

By how much does the velocity of Delphine and her board change during the hit? m/s

Delphine says, "I barely moved, so the board must have pushed on me much less than I pushed on it." Which response fits Newton's third law and the data?

A. The pushes were equal; she barely moved because her wheels were not turning.
B. She is right: the lighter board pushed with 1/25 of the force she pushed with.
C. She is right: the board pushed before the hit, and she pushed back after it.
D. The pushes were equal; she barely moved because her mass is 25 times as large.

10.

A parks worker says, "Put in the concrete curb. Concrete is so strong that it pushes on the board much harder than the board pushes on it, so the curb is safest and our bolts will be fine." Do you agree? Make a claim, use evidence from Table 1 and the criteria, and explain your reasoning with Newton's third law. Then recommend a stopper.