Question

A pendulum has a mass of m=2kg and a 1.0 m long string that is pulled back to an angle theta collides elastically with a mass M= 2kg, which is on the surface with a coefficent of friction of u=0.2. The mass M then slides fo delta x = 1.5 m before coming to rest. What is the initial angle theta?

Answer 1

a = - fk / m = - uk M g / M = - uk g = - 1.96 m/s^2

vf^2 - vi^2 = 2 a d

0^2 - v^2 = 2(-1.96)(1.5)

v = 2.43 m/s

for same mass elastic collision,

velocity exchanges.

now applying energy conservation,

m v^2 /2 = m g h

h = 2.43^2 / (2 x 9.81) = 0.3 m

h = L (1 - cos(theta))

0.3 = 1 (1 - cos(theta))

theta = 45.6 deg