Question

It takes 500 J of work to compress a spring 10 cm. What is the force constant of the spring?

a) 5 N/m
b) 2,000 N/m
c) 500 N/m
d) 50 N/m

Answer 1

The force constant of the spring can be calculated using Hooke's Law. In this case, 500 J of work is done to compress the spring by 10 cm. The force constant of the spring is 5,000 N/m.

Step-by-step explanation:

The force constant of a spring can be calculated using Hooke's Law:

F = kx

Where F is the force applied to the spring, k is the force constant, and x is the displacement of the spring. In this case, 500 J of work is done to compress the spring by 10 cm. Work is calculated by:

Work = (1/2)kx^2

Plugging in the given values, we can solve for k:

500 J = (1/2)k(0.1 m)^2

Simplifying the equation, we find that the force constant of the spring is 5,000 N/m. Therefore, the correct answer is d) 50 N/m.