# Quick K.E. Question

Hi I just have a quick question about Kinetic Energy.

If we imagine an asteroid in empty space with no gravity field acting on it, i.e. it's just in empty space moving along according to Newtons 1st Law i.e. with constant velocity.

Imagine a ship extends a magical robotic hand and exerts a force on the asteroid for a few seconds before letting it go, I want to know what happens.

I would say that because K_2 - K_1 = ½mv² - ½mv_0² = Fd the asteroid will have a higher kinetic energy at the end when the robotic arm lets go.

1: But, say an hour later, the asteroid will still be moving forward, will it still have the same kinetic energy as it did when it was released from the robotic arm?
No force is acting on it so no work is done but does the asteroid still have kinetic energy?

2: Also, if I use the kinetic energy as the asteroid is moving, well after it has been released, I will get the answer that the ship has no kinetic energy, what is wrong here?
Does something have kinetic energy only while a force acts on it?

I know it will have momentum as it moves but what about kinetic energy?

cepheid
Staff Emeritus
Gold Member
1: But, say an hour later, the asteroid will still be moving forward, will it still have the same kinetic energy as it did when it was released from the robotic arm?

Yes. Energy is conserved. It doesn't just disappear.

No force is acting on it so no work is done but does the asteroid still have kinetic energy?

The work done is equal to the CHANGE in kinetic energy. If no work is done, the kinetic energy will remain the same. It won't change. That's why it will be exactly the same one hour later.

2: Also, if I use the kinetic energy as the asteroid is moving, well after it has been released, I will get the answer that the ship has no kinetic energy, what is wrong here?

I don't understand what you mean. Can you explain more clearly what exactly you are trying to compute?

Does something have kinetic energy only while a force acts on it?

No, a force is not required! As the formula for kinetic energy that you posted clearly shows, if something has velocity, it has kinetic energy. Kinetic means "having to do with motion", and kinetic energy is the energy associated with motion. If something is moving, it has kinetic energy.

does the force exerted by the robotic arm lead to a change in velocity? so wont there b a change in KE

Hi thanks for the informative answer.

Well yeah, while the robotic arm exerts a force on the asteroid it will accelerate the asteroid forward for say 5 seconds, initially the asteroid has velocity $$v_1$$ and then after the robotic arm lets go 5 seconds later the asteroid moves forwards faster with velocity $$v_2$$.

My second part was unclear, sorry about that. I've got it now I was just confused for one second after reading a quack paper on kinetic energy.