A thin stick of mass M = 2.0 kg and length L = 2.6 m is hinged at the top. A piece of clay, mass m = 1.0 kg and velocity V = 0.9 m/s hits the stick a distance x = 1.90 m from the hinge and sticks to itWhat is the ratio of the final mechanical energy to the initial mechanical energy?
angular momentum is constant
energy goes down
Initial L around hinge = I omega of stick + m v R of clay
I = (1/3) * 2.0 * 2.6^2 * 0 + 1.0 * 0.9 * 1.90 = 1.71 kg m^2/s
Final L = 1.71 = 4.51 omega + 1.0 * 1.9^2 omega= (4.51+.0361)omega
= 8.12 omega
omega = .211 radians/s
initial Ke = (1/2) m v^2 = (1/2)(1)(.81) = .405 Joules
final Ke = I omega^2
I = 4.51 (.211)^2 + .0361 (.211)^2 = .487 (.211^2) = .0217 Joules
.0217/.405 = 0.0536
in other words lost most of the Ke in the collision