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.