Question

A student compresses the spring in a pop-up toy a distance of 0.02 m. If 0.068 J of energy are stored in the toy, what is the toy's spring constant?

1) 120 N/m
2) 170 N/m
3) 225 N/m
4) 340 N/m

Answer 1

To find the toy's spring constant with 0.068 J of energy stored over a compression distance of 0.02 m, the spring constant formula is used, which gives a spring constant of 340 N/m.

Step-by-step explanation:

To determine the spring constant of the pop-up toy given that 0.068 J of energy are stored when the spring is compressed a distance of 0.02 m, we can use the formula for elastic potential energy stored in a spring:

E = 1/2 * k * x^2,

where E is the energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position. We can solve for k:

k = 2 * E / x^2,

k = 2 * 0.068 J / (0.02 m)^2,

k = 2 * 0.068 J / 0.0004 m^2,

k = 0.136 J / 0.0004 m^2,

k = 340 N/m.

The spring constant of the toy's spring is therefore 340 N/m.