Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.55 cm, its potential energy is 0.0035 J.
What is the force constant of the spring?
What compression is required for the spring potential energy to equal 0.0094 ?
To find the force constant of the spring, we can use the formula for potential energy stored in a spring:
Potential energy (PE) = (1/2) * force constant (k) * compression^2
We are given that the potential energy is 0.0035 J and the compression is 0.55 cm.
Substituting these values into the formula, we get:
0.0035 J = (1/2) * k * (0.55 cm)^2
First, let's convert the compression of the spring into meters:
0.55 cm = 0.55 cm * (1 m / 100 cm) = 0.0055 m
Now we can rearrange the equation to solve for the force constant:
k = (2 * PE) / compression^2
= (2 * 0.0035 J) / (0.0055 m)^2
= 0.0035 J / (0.0055 m)^2
Calculating this expression, we find that the force constant of the spring is approximately 113.42 N/m.
To find the compression required for the spring potential energy to equal 0.0094 J, we can rearrange the formula as:
compression = sqrt((2 * PE) / k)
Substituting the given values:
compression = sqrt((2 * 0.0094 J) / 113.42 N/m)
= sqrt(0.0188 J / 113.42 N/m)
Evaluating this expression, we find that the required compression for the spring potential energy to equal 0.0094 J is approximately 0.0305 m or 3.05 cm.