what is the force constant of an ideal spring if 1.02J are stored in the spring when it is compressed 0.22m

1 answer

To determine the force constant (k) of an ideal spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In mathematical terms, this can be expressed as:

F = -kx

where F is the force applied to the spring, k is the force constant, and x is the displacement of the spring.

Given that 1.02 J of energy are stored in the spring when it is compressed by 0.22 m, we can use the formula for potential energy stored in a spring:

PE = (1/2)kx^2

where PE is the potential energy stored in the spring.

Setting the potential energy equal to 1.02 J and the displacement (x) equal to 0.22 m, we can solve for k:

1.02 J = (1/2)k(0.22 m)^2

1.02 J = (1/2)k(0.0484 m^2)

Simplifying:

1.02 J = 0.0242 k

k = 1.02 J / 0.0242

k ≈ 42.15 J/m

Therefore, the force constant of the ideal spring is approximately 42.15 J/m.