The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing?

Question

Quizplus · Accepted Answer

At point A (the release point), the ball has zero kinetic energy and zero potential energy. As it swings down to point B, it gains kinetic energy and loses potential energy. By the time it reaches point B, it has converted all of its potential energy to kinetic energy. Therefore, we can use conservation of energy to find the speed at point B.

Gravitational potential energy at A = mgh
Gravitational potential energy at B = 0

Therefore, the gain in kinetic energy = loss in potential energy
1/2mv^2 = mgh
v = sqrt(2gh)

Since the length of the string is 50 cm = 0.5 m, the height difference between A and B is h = 0.5 – 0.5cos(60) = 0.25 m

Plugging in the values, we get:
v = sqrt(2 x 9.8 x 0.25) = 3.14 m/s

Rounding to one significant figure, the answer is 3.1 m/s, which corresponds to choice C.

The String in the Figure Is 50 Cm Long