Coupling Model Rail Cars: A Science Fair Test of Force Pairs

Use collision data to apply Newton's third law and choose a gentle coupler.

The collision tests

Read the project board and Table 1, then answer the questions.

Science Fair Board: When Rail Cars Couple

1In a rail yard, freight cars are joined into trains by rolling one car into a parked car, so that the couplers on their ends snap together. Eighth graders Odalys Ferreira-Quinn and Bastian Rautio saw this at the model railroad club where Bastian volunteers. When a light car rolled into a heavy loaded car, the light car jolted hard and its little load of wooden crates often tipped over, while the heavy car barely moved. Bastian guessed that the heavy car pushed harder. For the science fair, the pair asked two questions: When two cars collide, does one push harder than the other? And what kind of coupler joins the cars gently?

2Club member Mr. Emeka Lindstrom lent them two low-friction lab carts and a level track. The moving car had a mass of 0.50 kg. The parked car was loaded with metal blocks to a mass of 1.50 kg. A spring launcher sent the moving car toward the parked car at 0.40 m/s in every trial. A force sensor on the front of each car recorded the push on that car 1,000 times a second, so the pair could find the largest push, called the peak force. Motion sensors at both ends of the track measured each car's speed just after the collision.

3The pair fitted six kinds of fronts to the two cars, one kind at a time. Hard plastic faces just bump. Spring bumpers squash and spring back. Grip strips are hook-and-loop tape that grabs and holds, and the pair tried them on hard faces, on rubber pads and on soft foam pads. The last design used magnets that push each other away, so the cars slowed and turned back before they touched. Each design was tested three times, and Table 1 shows the averages.

4In Table 1, "back" means the car rolled back toward the launcher after the collision. When a car turns around, the change in its speed counts the reversal. For example, going from 0.40 m/s forward to 0.20 m/s back is a change of 0.60 m/s.

5The club set two criteria for a new coupler. First, the cars must stay joined after they collide. Second, the peak force on each car must be no more than 10 N, so the crates stay upright.

Table 1. Moving car (0.50 kg) at 0.40 m/s hits parked car (1.50 kg)
Front design	Force on moving car (N)	Force on parked car (N)	Moving car after (m/s)	Parked car after (m/s)	Joined?
A. Hard faces	60	60	0.05 back	0.15	No
B. Spring bumpers	15	15	0.20 back	0.2	No
C. Grip strips on hard faces	40	40	0.1	0.1	Yes
D. Grip strips on foam	4	4	0.1	0.1	Yes
E. Pushing magnets	2	2	0.20 back	0.2	No
F. Grip strips on rubber	7	7	0.1	0.1	Yes

Which statement does Table 1 support?

A. The two pushes were equal with soft fronts but not with hard faces.
B. The moving car pushed harder, because it was moving before the collision.
C. The heavier parked car pushed about 3 times as hard on the moving car.
D. In each design, the two cars pushed on each other with equal peak forces.

Use design C. Both cars ended up rolling forward together.

The moving car's speed changed by m/s, and the parked car's speed changed by m/s.

Use design B and paragraph 4.

The moving car's speed changed by m/s, and the parked car's speed changed by m/s.

In every design, the moving car's speed changed about 3 times as much as the parked car's. Which explanation fits the data best?

A. The moving car felt its push first, and the parked car felt its push a moment later.
B. The launcher kept pushing the moving car during the collision, which added to its change.
C. The moving car has one third of the parked car's mass, so the same force changes its motion more.
D. The parked car pushed 3 times as hard, because it carries 3 times as much mass.

In design E, the magnet on the moving car pushes the parked car forward with a peak force of 2 N, and the cars never touch. What is the other force in this force pair?

A. The parked car's magnet pushes the moving car backward with 2 N.
B. The parked car's magnet pushes the moving car forward with 2 N.
C. The track pushes up on the parked car with a force of 2 N.
D. The parked car pushes back with a force smaller than 2 N.

The pair takes the blocks off the parked car, so both cars have a mass of 0.50 kg. They repeat design C. Which prediction fits Newton's third law and the pattern in Table 1?

A. The forces will be equal, and the two cars' speeds will change by about the same amount.
B. The moving car will push harder, so the parked car's speed will change more.
C. The forces will be equal, but the moving car's speed will still change 3 times as much.
D. The parked car will push harder, so the moving car will roll back toward the launcher.

Choosing a coupler

Use Table 1 and the club's criteria in paragraph 5.

Circle every design that meets both of the club's criteria.

ABCDEF

Designs C and D both joined the cars, which then rolled at 0.10 m/s. Why was the peak force so much smaller with foam?

A. The foam took some of the moving car's mass, so less mass hit the parked car.
B. The foam squashed, so the cars slowed over a longer time with smaller pushes.
C. The foam slowed the moving car before the launch, so it arrived much slower.
D. The foam made the parked car push back on the moving car less than it was pushed.

Design E had the smallest peak force. Why should the club still not use it as a coupler?

A. Its magnets pushed harder on the parked car than on the moving car.
B. Its peak force of 2 N is above the club's limit of 10 N.
C. The cars bounced apart, so they did not stay joined.
D. The parked car stayed at rest, so no train was formed.

10.

In a real rail yard, a 30,000 kg car rolls into a parked 90,000 kg car on level track, and the couplers join. At one moment, the moving car pushes forward on the parked car with a force of 300,000 N.

At that moment, the parked car pushes backward on the moving car with a force of N.
Over the whole collision, the moving car's speed drops by 1.2 m/s. The parked car's speed rises by about m/s.

11.

Bastian still says, "The light car jolts more because the heavy car pushes on it harder." Is he right? Make a claim, give evidence from Table 1, and explain your reasoning with Newton's third law. Then say which design the club should use and why.