Question

A pendulum is swinging back and forth with no non-conservative forces acting on it. At the highest points of its trajectory, the kinetic energy of the pendulum bob is instantaneously equal to zero joules. At the lowest point of its trajectory, the potential energy is instantaneously equal to zero joules. Which one of the following expressions describes the kinetic and potential energies at the point mid-way between to the highest and lowest points?
a. K = 0, U = Umax
b. K = U
c. K < U
d. K > U
e. U = 0, K = Kmax

Answer 1

Answer:

b. K = U

Explanation:

In this case you have that there are no non-conservative forces over the pendulum. Hence, the total mechanical energy if the pendulum must conserve. You take into account that the potential and kinetic energy of a pendulum are given by:

$E_T=K+U=\frac{1}{2}mv^2+mgh$

m: mass of the pendulum

h: height of the pendulum

v: speed

In each moment of the trajectory of the pendulum ET does not change.

You have that, at the lowest point U=0J  and for the highest point K=0J. For that point K=ET and U=ET respectively.

Hence, for a mid-way between those points it is necessary that:

b. K = U