Physics Online Quiz Question on Momentum

[okgo]

Homework Statement

A 7 kg glider on an air track starts with an initial velocity of 32 m/s and then runs into a 2 kg glider which is initially at rest. During the collision, which glider has a larger magnitude change in momentum?

Homework Equations

It's a new chapter and the teacher wants us to read before the class, alas he makes us do a quiz . I'm not really sure of my answer below. It is a free-response quiz.

The Attempt at a Solution

Each glider applies an equal and opposite force, but the smaller glider will undergo a larger acceleration as acceleration is inversely proportional to the mass. Both objects experience a different change in momentum due to the different accelerations experienced by both gliders. But momentum is conserved. This means the total change in momentum of the two glider system is zero. The vector addition of the momentum vectors (after collision) of each glider will be equal in magnitude and direction to the initial momentum vector (before the collision).

 

[LowlyPion]

Homework Statement

A 7 kg glider on an air track starts with an initial velocity of 32 m/s and then runs into a 2 kg glider which is initially at rest. During the collision, which glider has a larger magnitude change in momentum?

Homework Equations

It's a new chapter and the teacher wants us to read before the class, alas he makes us do a quiz . I'm not really sure of my answer below. It is a free-response quiz.

The Attempt at a Solution

Each glider applies an equal and opposite force, but the smaller glider will undergo a larger acceleration as acceleration is inversely proportional to the mass. Both objects experience a different change in momentum due to the different accelerations experienced by both gliders. But momentum is conserved. This means the total change in momentum of the two glider system is zero. The vector addition of the momentum vectors (after collision) of each glider will be equal in magnitude and direction to the initial momentum vector (before the collision).

Momentum is conserved. You are correct. Whatever one gains the other must lose.

 

[sungod]

It seems to me that they would both have the same magnitude change. If the initial momentum vector has a length n (224 in this case), then the final momentum vector also has a length n. This length n is made up of the length of the vector of the final momentum of the 7kg glider and the length of the vector of the momentum of the 2 kg glider (assuming they don't stick). Say the length of the final momentum vector, the magnitude of the final momentum, of the 7kg glider is a and that of the 2 kg glider is b, then n = a + b. But since the 2 kg glider had no momentum to begin with, it's change in momentum is b. While the 7 kg glider started with momentum n and ended up with momentum a, so its change in momentum is n-a = b.