Ten sense-making tasks on momentum, impulse, and collisions. Explain your reasoning for every answer. The explanation counts as much as the answer.
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Each cart rolls along a level track and hits a wall. The cart's mass, its velocity just before the collision, and its velocity just after are shown. Some carts stick to the wall; others bounce back.
Rank the carts by the magnitude of the impulse the wall exerts on the cart, from greatest to least. If any are equal, show the tie. If the ranking cannot be determined, say so.
Greatest 1 ____ 2 ____ 3 ____ 4 ____ 5 ____ 6 ____ Least
Explain your reasoning.
Back to topA 6000 kg truck and a 1500 kg car, each moving at 20 m/s, collide head-on. Three students discuss what happens during the collision.
Ava: "The truck exerts a bigger force on the car than the car exerts on the truck, because the truck has more mass."
Ben: "The forces are equal, so the changes in momentum are equal in size. But the car's change in velocity is four times bigger."
Cam: "The car's change in momentum is bigger, because it gets wrecked and thrown backward."
Which student(s), if any, do you agree with? Explain what is right or wrong about each statement.
Back to topCart A (2.0 kg) moves to the right at 3.0 m/s. Cart B (1.0 kg) moves to the left at 3.0 m/s. They collide on a frictionless track and stick together. Right is positive.
A student draws these momentum bar charts and concludes that the carts move to the right at 3.0 m/s after the collision:
What, if anything, is wrong with the bar charts or the conclusion? If something is wrong, explain the error, draw the correct charts, and find the correct final velocity. If nothing is wrong, explain why.
Back to topFor each system and process, choose:
A. the system's momentum is conserved B. the system's momentum is not conserved C. cannot be determined
| System and process | Choice |
|---|---|
| (a) System: a ball, as it falls freely | |
| (b) System: the ball and Earth, as the ball falls freely | |
| (c) System: two carts, as they collide on a level frictionless track | |
| (d) System: just one of those two carts, during the collision | |
| (e) System: a car, as it brakes to a stop on a road | |
| (f) System: all the pieces of a firework, during the brief instant it explodes | |
| (g) System: two carts colliding on a track, with no information about friction or the track's tilt |
Explain the rule you used. For every "not conserved" answer, name the external force responsible.
Back to topA 0.20 kg ball of putty and a 0.20 kg rubber ball each hit a wall at 10 m/s. The putty sticks. The rubber ball bounces straight back at 10 m/s. Each collision lasts 0.010 s.
For each quantity, state whether it is greater for the putty, greater for the rubber ball, or the same for both. If it's different, give the ratio.
| Quantity | Answer |
|---|---|
| (a) Magnitude of the ball's change in momentum | |
| (b) Magnitude of the impulse the wall exerts on the ball | |
| (c) Average force the ball exerts on the wall | |
| (d) Kinetic energy lost by the ball |
Explain each answer. Which ball is better at knocking over a block of wood? Why?
Back to topA 1.0 kg cart and a 3.0 kg cart are at rest on a frictionless track, held together by a thread with a compressed spring between them. The thread is burned and the carts fly apart.
The equation below was written by a student solving a collision problem:
$$(3.0\ \text{kg})(4.0\ \text{m/s}) + (2.0\ \text{kg})(-1.0\ \text{m/s}) = (3.0\ \text{kg})(0.50\ \text{m/s}) + (2.0\ \text{kg})\,v$$
A 0.60 kg ball is at rest on a tee. A bat hits it, and the graph shows the force on the ball during the hit.
A 2.0 kg cart moving at 6.0 m/s hits a 1.0 kg cart at rest on a frictionless track. The carts stick together. Find their speed after the collision.
Student solution:
Energy is conserved, so $K_{before} = K_{after}$.
$\tfrac12(2.0\ \text{kg})(6.0\ \text{m/s})^2 = \tfrac12(3.0\ \text{kg})v^2$
$36\ \text{J} = (1.5\ \text{kg})v^2 \quad\Rightarrow\quad v = 4.9\ \text{m/s}$
Identify the error in the solution. Explain the physics of why it's an error, then find the correct speed and the kinetic energy lost.
Back to topTwo 2.0 kg carts move toward each other, each at 3.0 m/s, on a frictionless track. They collide and stick together.
Jordan writes: $p_{total} = (2.0\ \text{kg})(3.0\ \text{m/s}) + (2.0\ \text{kg})(3.0\ \text{m/s}) = 12\ \text{kg·m/s}$, so after they stick, $v = \dfrac{12\ \text{kg·m/s}}{4.0\ \text{kg}} = 3.0\ \text{m/s}$.