A 0.10 meter spring is stretched from equilibrium to position A at 0.15 meters and then to Position B at 0.20 meters. Compared with the springs potential energy at A, why is the potential energy at B four times as great
The potential energy stored in a spring is given by the formula:
PE = 0.5 * k * x^2
where PE is the potential energy, k is the spring constant, and x is the displacement from equilibrium.
Since the spring is stretched from equilibrium to position A at 0.15 meters and then to position B at 0.20 meters, the displacements are 0.15 meters and 0.20 meters respectively.
Let's say the potential energy at position A is PE_A and the potential energy at position B is PE_B.
So, PE_A = 0.5 * k * (0.15)^2
PE_B = 0.5 * k * (0.20)^2
To find out why the potential energy at B is four times greater than the potential energy at A, we can compare the two energies:
PE_B = 4 * PE_A
0.5 * k * (0.20)^2 = 4 * (0.5 * k * (0.15)^2)
0.5 * k * 0.04 = 2 * (0.5 * k * 0.0225)
0.02 * k = 2 * 0.01125 * k
0.02 = 0.0225
As seen in the equation above, the potential energy at B is four times as great as the potential energy at position A because the square of the displacement at B is four times the square of the displacement at A.