Rocket Club: Force Pairs at Launch and Landing

Use Newton's third law to explain a launch and design a safer landing.

Answer Key

Launch day

Read the club update and answer the questions.

Rocket Club Update: Up and Down

1The Ridgeview Middle School Rocket Club launches water rockets made from 2-liter plastic bottles. Each rocket is partly filled with water and set nose-up on a launch pad. The club's advisor, Mr. Haruto Sato, pumps air into the bottle while everyone stands well back. When he pulls the release cord, the pressurized air shoves the water out of the nozzle at the bottom, and the rocket shoots upward.

2Club president Amara Lindqvist used a force sensor on a test stand to study the launch. At one moment the rocket was pushing on the water with a force of 40 N, straight down. In slow-motion video of a real launch, the water sprayed toward the ground in a fast jet while the rocket sped off in the opposite direction. After the water ran out, the rocket coasted upward for a moment, slowed down, and then drifted back to the field under its parachute.

3This year the club wants to carry a small sensor capsule in the nose and bring it back undamaged. In early tests, the capsule often slammed into the ground hard enough to crack its circuit board. To study the problem safely indoors, the club used a 0.5 kg lab cart in place of the capsule. In every trial the cart rolled at 1.0 m/s along a flat track and hit a solid wall. One force sensor was mounted on the front of the cart and another on the wall, so the club could measure the push on each object during the crash. They changed only the bumper on the front of the cart. Each bumper was tested three times, and the table shows the average of the three trials. The sensors recorded the force many times each second, so the club could find both the largest force during the crash, called the peak force, and how long the cart stayed in contact with the wall.

4The circuit board is likely to crack if the peak force on it goes above 30 N. The capsule also has a tight weight limit: any bumper must have a mass of 15 g or less, or the rocket will not fly high enough for the parachute to open.

During the launch, the rocket pushes the water down. Which force is the other half of this force pair?

A. The air outside pushes down on the rocket's nose.
B. The water pushes the rocket up.
C. Earth pulls the rocket down toward the ground.
D. The launch pad pushes the rocket up before liftoff.

Use paragraph 2.

At that moment, how large is the force of the water on the rocket? 40 N

Sort each pair of forces. A third-law pair is two forces that two objects exert on each other.

The cart pushes on the wall; the wall pushes on the cart.Earth pulls the resting rocket down; the launch pad pushes the rocket up.The capsule pushes down on the ground; the ground pushes up on the capsule.The parachute pulls up on the capsule; Earth pulls down on the capsule.The rocket pushes the water down; the water pushes the rocket up.

Third-law force pair	Not a third-law pair
The cart pushes on the wall; the wall pushes on the cart. The capsule pushes down on the ground; the ground pushes up on the capsule. The rocket pushes the water down; the water pushes the rocket up.	Earth pulls the resting rocket down; the launch pad pushes the rocket up. The parachute pulls up on the capsule; Earth pulls down on the capsule.

Designing a safer landing

Use the crash test table and the club update to answer the questions.

Cart crash tests (0.5 kg cart at 1.0 m/s)
Bumper	Bumper mass (g)	Peak force on cart (N)	Peak force on wall (N)	Contact time (s)
None (hard plastic)	0	110	110	0.01
Rubber pad	12	45	45	0.025
Foam block	8	22	22	0.05
Folded paper cone	20	14	14	0.08

Which result in the table is evidence for Newton's third law?

A. In each trial, the cart and the wall felt forces of the same size.
B. The heaviest bumper gave the largest force on the cart.
C. The wall felt no force, because the wall did not move.
D. With a soft bumper, the cart felt a bigger force than the wall.

The peak force on the cart with no bumper is how many times the peak force with the foam block? 5 times

Which explanation of the foam block's lower peak force fits the data best?

A. The foam makes the cart push less on the wall than the wall pushes on the cart.
B. The foam adds mass to the front of the cart, so the cart hits the wall with less speed.
C. The foam squashes, so the crash lasts longer and the push is spread out over more time.
D. The foam soaks up the push, so the wall does not push back on the cart.

Which bumper meets both of the club's requirements from paragraph 4?

A. Foam block
B. Folded paper cone
C. Rubber pad
D. No bumper

On another test, the 0.5 kg cart rolls head-on into a heavier 2 kg cart. Which statement about the forces during the crash is correct?

A. The lighter cart pushes harder, because it was the one moving.
B. The forces cancel out, so neither cart's motion changes.
C. The heavier cart pushes harder, because it has more mass.
D. Each cart pushes on the other with the same size force, in opposite directions.

A club member says, "The foam block works because it makes the wall push back on the cart less than the cart pushes on the wall." Is this right? Make a claim, use evidence from the table, and explain your reasoning with Newton's third law. Then say which bumper the club should use.

Claim: The club member is wrong about why the foam works. Evidence: with the foam block, the peak force on the cart and the peak force on the wall were both 22 N, and in every trial the two forces were equal. With no bumper both were 110 N. Reasoning: Newton's third law says the cart and the wall push on each other with equal and opposite forces, so foam cannot make one push smaller than the other. Instead, the foam squashes, the contact time grows from 0.010 s to 0.050 s, and both forces become smaller. The club should use the foam block, because its peak force of 22 N is under 30 N and its mass of 8 g is under the 15 g limit.