one-sided force applied to spring

snoopies622

In a place with no friction, I have a rocket that applies a constant force f to a weight of mass m, and between them is a spring with constant k. I assume that the mass of the spring is negligible.

As the three objects accelerate, by how much does the spring contract? My intuition tells me that the greater the mass of the weight, the more the spring contracts, but I don't see how this works out algebraically.

Hassan2

Hi snoopies622,

Your intuition is wrong. The change in the spring length depends on the force F and the constant K as simply as:

Δx=F/K

when m in your problem is small, it accelerates faster , trying to make the length shorter, so you need to move the point of force faster to keep the length ( and force) constant.