# Confused why momentum is conserved in 2 falling bodies problem [duplicate]

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I was doing a physics problem out of my textbook, which could paraphrased as follows:

There’s a frame suspended at rest from a coiled spring. A mass of flexbile putty is dropped onto the frame, causing the frame and putty to move downwards together. What is the maximum distance the frame goes downward?

The problem could clearly modeled as a collision followed by an energy conservation problem.

However, after thinking about it, I couldn’t come up with a justification why momentum should be conserved in this inelastic collision, considering that the net external forces on the frame-putty system are not zero (putty experiences gravitational force, frame experiences gravitational and elastic, right?).

After reviewing the solution, they give no justification why momentum should be conserved in this case, but they utilize an inelastic collision with momentum conservation.

Any thoughts on what I’m missing here?

## marked as duplicate by sammy gerbil, Kyle Kanos, user191954, rob♦Nov 9 '18 at 22:00

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## 1 Answer

I couldn’t come up with a justification why momentum should be conserved in this inelastic collision, considering that the net external forces on the frame-putty system are not zero (putty experiences gravitational force, frame experiences gravitational and elastic, right?).

You are right. Momentum is only conserved when the net external force is zero. If the net external force is nonzero then the change in momentum is given by the impulse: $$\Delta p = \int F \; dt$$. Since F is nonzero then $$\Delta p$$ is also nonzero.

However, note that the impulse is an integral over time. The time of the collision is very brief, so even though the impulse is not zero it will still be very small. So the unstated justification is that the duration of the collision is so brief that the impulse from the external forces is negligible. It is not zero, but just small enough to ignore.