A block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case?

x₂ =6*x₁

Explanation:

In absence of friction, along a horizontal surface, all the elastic potential energy stored in the spring becomes kinetic energy, so we can write the following expression for the first case:

       

In the second case, we have a mass 4m, which reaches to a speed 3v due to the energy stored in the spring.We can write the same equation than for (1) replacing m by 4m and v by 3v, as follows:

       

Dividing (2) over (1) on both sides, and rearranging terms, we get:

       

Taking square roots on both sides, we get:x₂ = 6*x₁So, in this case, the spring was compressed six times the distance that was compressed in the first case.

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