A question about Momentum and kinetic energy.

[ZARATHUSTRA]

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]

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.

 

[ZARATHUSTRA]

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!

 

[HalfLostAndSearching]

I can explain the concepts of momentum and kinetic energy in this scenario. Momentum is a measure of an object's mass and velocity, and it is conserved in a closed system. This means that in the absence of external forces, the total momentum of the system remains constant.

In the given scenario, the two masses colliding and sticking together can be considered a closed system, as there are no external forces acting on them. Therefore, the total momentum of the system before and after the collision will remain the same.

Kinetic energy, on the other hand, is not always conserved in a closed system. In this scenario, the kinetic energy of the system will decrease as the spring compresses and the two masses come to a stop. This is because some of the kinetic energy is converted into potential energy stored in the compressed spring.

The statement about the spring force being an internal force and not changing the net linear momentum is referring to the fact that the spring force acts on both masses equally and in opposite directions, thus canceling out any change in momentum. The same principle applies to the example of throwing a rock at a wall - the force of the impact is an external force and can change the object's momentum.

In conclusion, the linear momentum of an object will be conserved in the absence of external forces, but the kinetic energy may not be conserved due to internal forces and energy conversions.