Question

A spring has a force constant of 40000 N/m.

How far must it be stretched for its potential energy to be 42 J?
Answer in units of m

Answer 1

To have a potential energy of 42 J, a spring with a force constant of 40000 N/m must be stretched by 0.0458 meters (4.58 cm).

Step-by-step explanation:

To determine how far a spring with a force constant of 40000 N/m must be stretched for its potential energy to be 42 J, we can use the formula for the potential energy stored in a spring:

PE = (1/2) k x^2

Where PE is the potential energy, k is the force constant of the spring, and x is the displacement or stretch of the spring from its equilibrium position.

Rearranging the formula to solve for x, we get:

x = √(2 * PE / k)

Plugging in the given values:

x = √(2 * 42 J / 40000 N/m)

x = √(84 / 40000)

x = √0.0021

x = 0.0458 meters, or 4.58 cm

The spring must be stretched 0.0458 meters to have 42 J of potential energy.

Answer 2

0.05m

Step-by-step explanation:

Given parameters:

Force constant of the spring = 40000N/m

Potential energy = 42J

Unknown:

Extension = ?

Solution:

To solve this problem, use the expression below:

E.PE =
`(1)/(2)` k e²

k is spring constant

e is the extension

42 =
`(1)/(2)` x 40000 x e²

e = 0.05m