A student uses a spring with a spring constant of 130 N/m in his projectile apparatus. When 56 J of potential energy is required to launch the projectile to a certain height, what is the compression in the spring?
To find the compression in the spring, we can use the formula for potential energy stored in a spring.
The formula for potential energy stored in a spring is:
PE = (1/2)kx^2
Where:
PE is the potential energy stored in the spring (in joules)
k is the spring constant (in newtons per meter)
x is the compression or extension of the spring (in meters)
In this case, we are given the potential energy (PE) as 56 J and the spring constant (k) as 130 N/m.
Substituting these values into the formula, we have:
56 J = (1/2)(130 N/m)(x^2)
To find the compression (x), we need to rearrange the equation to solve for x:
x^2 = (2 * 56 J) / (130 N/m)
Simplifying the equation,
x^2 = 112 J / 130 N/m
x^2 = 0.861 m
Taking the square root of both sides,
x ≈ √0.861 m
x ≈ 0.929 m
Therefore, the compression in the spring is approximately 0.929 meters.