Greater change in momentum between two objects

[positron]

When two objects collide, how do you determine which object experiences the greater change in momentum? for instance, if A and B with different masses traveling at different speeds collide, do they experience the same momentum change after the collision? What about KE?

This is my reasoning so far:
The change in momentum does not change, because the same force acts on both A and B for the same amount of time during the collision. However, the kinetic change because the masses of the objects are different even though the change in velocities are the same. Is this correct?

 

[Diane_]

You've correctly noted that the same force is acting on both A and B. It will obviously also act for the same amount of time, meaning the impulse imparted to each will be the same, give or take a direction. What is impulse, and what does this tell you about the momentum change for each block? And, if their masses are different, what does this tell you about the velocity change for each block?

Once you have that, consider that kinetic energy is linear in mass but quadratic in speed - what does that tell you about the change in kinetic energy for each block? It might be a good time here to write a few equations and calculate the ratios of the kinetic energy for each block before and after the collision. What do those ratios depend on?

Bottom line: You're making a couple of bad assumptions, but apart from those your reasoning isn't bad. Go back and look at the definition and defining equations for impulse, momentum and kinetic energy.

 

[quicknote]

Your reasoning is partially correct. The change in momentum between two objects is determined by the force acting on them and the duration of the collision. If the same force acts on both objects for the same amount of time, then the change in momentum will be the same for both objects. However, the final momentum of each object will be different due to their different masses and velocities.

To determine which object experiences the greater change in momentum, you would need to compare the initial and final momenta of each object. The object that experiences a greater change in momentum will have a larger difference between its initial and final momenta.

Regarding kinetic energy (KE), this is also dependent on the mass and velocity of the objects. The formula for KE is 1/2 * mass * velocity^2. So, even if two objects experience the same change in velocity, their KE will be different if their masses are different. In your example, object B with a larger mass will have a higher KE than object A with a smaller mass, even if they experience the same change in velocity. This is because KE takes into account both the mass and velocity of an object, whereas momentum only considers the mass and velocity in the direction of motion.