It takes 7.9 J of work to stretch a spring 4.6 cm from its unstressed length. How much (in J) spring potential energy is then stored by the spring?
To find the spring potential energy stored by the spring, you can use the formula:
Potential Energy (PE) = (1/2) * k * x^2
where PE is the potential energy stored by the spring, k is the spring constant, and x is the displacement of the spring from its unstressed length.
In this case, the work done to stretch the spring is given as 7.9 J, which is equal to the potential energy stored by the spring. We need to solve for the potential energy, so let's rearrange the formula:
PE = (1/2) * k * x^2
Given that the displacement x is 4.6 cm, we need to convert it to meters by dividing it by 100:
x = 4.6 cm / 100 = 0.046 m
Now we can rearrange the formula again and solve for k:
k = (2 * PE) / x^2
Substituting the given values:
k = (2 * 7.9 J) / (0.046 m)^2
Simplifying further:
k = 2 * 7.9 J / 0.002116 m^2
k = 7471.06 N/m
Now that we have the spring constant k, we can determine the potential energy stored by the spring using the original formula:
PE = (1/2) * k * x^2
Substituting the values:
PE = (1/2) * 7471.06 N/m * (0.046 m)^2
PE = 7.9 J
Therefore, the spring potential energy stored by the spring is 7.9 J.