Question

examine the diagram of a swinging pendulum
to start its swinging, the pendulum was pulled up to position a and then released. at which position(s) is the pendulums kinetic energy at a minimum and its gravitational potential energy at a maximum?
a) position c only
b) position e only
c) positions b and c
d) positions a and e

Explanation:

Step1: Recall energy concepts

Kinetic energy ($KE=\frac{1}{2}mv^{2}$) depends on speed. Gravitational potential energy ($PE = mgh$) depends on height. At maximum height, speed is minimum (ideally zero at extreme points in a simple pendulum model).

Step2: Analyze positions

• Position \(A\) and \(E\) are at the highest points. At these points, the pendulum's speed \(v = 0\) (momentarily stops before changing direction), so \(KE=\frac{1}{2}m(0)^{2}=0\) (minimum kinetic energy).
• Using \(PE=mgh\), since \(h\) (height from the lowest - point reference) is maximum at \(A\) and \(E\), gravitational potential energy is maximum.
• Position \(C\) is the lowest point. Here, \(h\) (for gravitational potential energy with respect to the lowest - point) is minimum (\(h = 0\) if we take \(C\) as the reference for height in the pendulum's motion), and speed is maximum (so \(KE\) is maximum).
• Positions \(B\) and \(D\) are intermediate points with non - zero speed (\(KE>0\)) and non - maximum height (\(PE < PE_{max}\)).

Answer:

D. positions A and E