Question

A spring of negligible mass has force constant k = 1700 N/m.

How far must the spring be compressed for an amount 3.30 of potential energy to be stored in it?

Answer 1

The spring with a spring constant of 1700 N/m must be compressed by 6.23 cm to store 3.30 J of potential energy.

Step-by-step explanation:

To determine how far a spring must be compressed to store a given amount of potential energy, we use the formula for elastic potential energy in a spring: U = 1/2 k x^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

In this case, we are given the spring constant k = 1700 N/m and the potential energy U = 3.30 J. To find the displacement x, we solve for x in the potential energy equation:

3.30 J = 1/2 (1700 N/m) x^2

Solving for x gives:

x = sqrt((2 * 3.30 J) / (1700 N/m))

x = sqrt((6.60 J) / (1700 N/m))

x = sqrt(0.00388235 m^2)

x = 0.0623 m or 6.23 cm

Therefore, the spring must be compressed by 6.23 cm to store 3.30 J of potential energy.