Suppose a 0.30-kg mass on a spring that has been compressed 0.20 m has elastic potential energy of 1.0 J.How much further must the spring be compressed to triple the elastic potential energy?

Question

Quizplus · Accepted Answer

The elastic potential energy stored in the spring can be given by:

PE = 0.5*k*x^2

where PE is the elastic potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

Given that the mass on the spring has an elastic potential energy of 1.0 J when it is compressed by 0.2 m, we can write:

1.0 J = 0.5*k*(0.2 m)^2

Solving for k, we get:

k = 25 N/m

Now, we need to find how much further the spring must be compressed to triple the elastic potential energy. Let's assume that the spring is compressed by x m from its equilibrium position to achieve this.

The new elastic potential energy stored in the spring can be given by:

PE' = 0.5*k*(x + 0.2 m)^2

We want PE' to be three times the original PE. Therefore, we can write:

3*1.0 J = 0.5*(25 N/m)*(x + 0.2 m)^2

Simplifying and solving for x, we get:

x = 0.15 m

Therefore, the spring must be compressed by an additional 0.15 m to triple the elastic potential energy stored in it. The best choice is B) 0.15 m.