# A question about Momentum and kinetic energy.

this question is from the book AP Physics C

A mass m1 initially moving at a speed v0 collides with and sticks to a spring attached to a second, initially stationary mass m2. the two masses continue to move to the right on a frictionless surface as the length of the spring oscillates. at the instant that the spring is maximally extended, the velocity of the first mass is ------------

regardless to the answer because it's not the problem i want to figure out, it's the conceptual problem.so the answer on the back is the momentum is conserved, but i wonder if the kinetic energy is conserved too(since it's spring related)? and i don't understand why they are saying" the spring force is an internal force, which does not change the net linear momentum." but i think if you throw a rock on the wall the linear momentum on the x-axis of the rock would lose, but there is no internal force on the rock on the x-axis(ignore the air resistance). in exactly, when and how would an object's linear momentum be conserved?

Stephen Tashi
i don't understand why they are saying" the spring force is an internal force, which does not change the net linear momentum."

Whether a force is "internal" depends on what "system" you are considering. If we think of the two masses and the spring as a single system, the force of the spring on the masses is "internal". If we are thinking of mass m1 as a "system" then the force of the spring is not "internal" to it.

but i think if you throw a rock on the wall the linear momentum on the x-axis of the rock would lose, but there is no internal force on the rock on the x-axis(ignore the air resistance). in exactly, when and how would an object's linear momentum be conserved?

If you consider the rock as the "system" then the force of the wall on the rock is not "internal". Momentum of a system is not conserved when net external forces act on it.

i wonder if the kinetic energy is conserved too(since it's spring related)?

I'm not sure what you mean by "since it's spring related". If you are asking whether kinetic energy would be conserved if the spring is an ideal type of massless spring that obeys Hooke''s law, I think it would be. We could try to analyze the situation and find out.

Bystander
Homework Helper
Gold Member
it's the conceptual problem

kinetic energy is conserved too(since it's spring related)?
For the ideal case Stephen has stated, yes.

the spring force is an internal force
To the system comprised of both masses and the spring.

when and how would an object's linear momentum be conserved?
Not "object," but "system." The linear momentum of the system is conserved if no outside forces are acting on it. In this case, you'll have to calculate the momenta of the components of the system and sum them for any given time of interest.

When i see there is a spring, i always have this acquiescence that the kinetic energy should be conserved. so anyway, thank you so much for helping me realize what the problem is , i understand now!