Final answer:
To calculate the spring constant and spring potential energy, you can use Hooke's law and the formulas F = kx and PEs = 1/2kx^2. The spring constant can be calculated using k = F/x, where F is the force and x is the displacement. The spring potential energy can be calculated using the formula PEs = 1/2kx^2.
Step-by-step explanation:
To calculate the spring constant and spring potential energy, we start by using Hooke's law, which states that the force needed to stretch or compress a spring is proportional to the distance it is stretched or compressed. Hooke's law is expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement. To calculate the spring constant, we can rearrange the equation to k = F/x. To calculate the spring potential energy, we use the formula PEs = 1/2kx^2, where PEs is the potential energy stored in the spring, k is the spring constant, and x is the displacement.
For example, if we have a spring with a mass of 0.02 kg and a stretched length of 0.028 m, we can calculate the spring constant and spring potential energy as follows:
Calculate the force using F = mg, where m is the mass and g is the acceleration due to gravity. F = (0.02 kg)(9.8 m/s^2) = 0.196 N
Calculate the spring constant using k = F/x. k = 0.196 N / 0.028 m = 7 N/m
Calculate the spring potential energy using PEs = 1/2kx^2. PEs = 1/2(7 N/m)(0.028 m)^2 = 0.00596 J