Energy of a Trolley Attached to a Spring

This is a conceptual question that was asked me about the energy of a trolley attached to a spring, moving on a frictionless horizontal surface.

Let’s say there’s a wall, with a spring attached to it, and a trolley attached to the spring. And the ground the trolley moves on is frictionless, and no air resistance etc… when I pull the spring to one direction, it’ll gain strain energy, yet they’ll be restoring forces acting on it trying to return it to its original position. So on release, the elastic potential energy is lost because the extension is decreasing, but since energy is conserved it’s converted to Kinetic energy.. so E.P.E is decreasing –> K.E is increasing, hence the trolley gains momentum, until eventually the spring goes back to its original shape where the restoring force stops acting and no net force acts and the trolley is at its max speed/velocity, then it continues to move forward because… it still has momentum? and by newtons first law, it’ll keep moving in a straight line.. and since it still has kinetic energy, it moves forward.. but as the spring compresses again it loses it in the form of strain energy.. and that happens until all k.e. –> strain energy and it comes momentarily to rest and then restoring force is dominant and it moves backwards and oscillates to and fro forever…
But if that’s true, why doesn’t the trolley move backwards right away, the moment that the restoring force acts on it? what keeps it moving forward? I’m quite confused in that.. Is it the trolley’s inertia?


Well, most of the description of what is going on with the trolley and the spring, especially in the beginning, is correct. Stretching the spring gives it potential energy; when it is released, that energy is transferred to the trolley as kinetic energy. In terms of forces, there is a restoring force pulling the spring back towards the equilibrium position, which makes the trolley move back.

When the spring goes back to the original length, there is no force on it, (yes, it has maximum speed) but it continues to move because of Newton’s first law. The spring then compresses and absorbs the kinetic energy, trolley comes to a momentary rest and starts moving again… The result is oscillations.

Coming to the actual question,

why doesn’t the trolley move backwards right away, the moment that the restoring force acts on it? what keeps it moving forward? I’m quite confused in that.. Is it the trolley’s inertia?

There are two ways of looking at this:

  1. In terms of energy: In order to change direction, the trolley needs to come to rest momentarily, having zero kinetic energy. However, the trolley already has kinetic energy as it is moving ‘forwards’.┬áThe restoring force works against the trolley and reduces this energy, but it takes some time to bring it to zero.
  2. In terms of forces: The restoring force is the only force acting on the trolley, in the opposite direction of its movement. Using Newton’s second law, this causes it to decelerate. It takes some time to reduce its velocity to zero and make it move with negative velocity.
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