Question

Consider a particle on which few conservative internal and few non-conservative intemal forces are acting. Then work done by the resultam non conservative force is equal to: (Extemal forces are

absent

(a) Change in Kinetic Energy

(b) Chunge in Potential Energy, (c) Change in Mechanical Energy

Answer 1

Explanation:

First, let us obtain an expression for the potential energy stored in a spring (PEs). We calculate the work done to stretch or compress a spring that obeys Hooke’s law. (Hooke’s law was examined in Elasticity: Stress and Strain, and states that the magnitude of force F on the spring and the resulting deformation ΔL are proportional, F = kΔL.) (See Figure 1.) For our spring, we will replace ΔL (the amount of deformation produced by a force F) by the distance x that the spring is stretched or compressed along its length. So the force needed to stretch the spring has magnitude F = kx, where k is the spring’s force constant. The force increases linearly from 0 at the start to kx in the fully stretched position. The average force is kx2kx2. Thus the work done in stretching or compressing the spring is Ws=Fd=(kx2)x=12kx2Ws=Fd=(kx2)x=12kx2. Alternatively, we noted in Kinetic Energy and the Work-Energy Theorem that the area under a graph of F vs. x is the work done by the force. In Figure 1c we see that this area is also 12kx212kx2. We therefore define the poten