5) A sphere A (of mass m) and sphere B (of mass 5m) are attached to the ceiling

Question

5) A sphere A (of mass m) and sphere B (of mass 5m) are attached to the ceiling by massless strings of identical length forming twin pendulums of length L. Sphere A is drawn to the left so that its center of mass has been raised a distance h and is then released. As sphere A moves back through equilibrium it hits and adheres sphere B. The combined system swings to the right, eventually reaching some maximum height before returning to equilibrium. Ballistic Pendulum 5m D To what maximum height will the combined system rise? Show your work. Express your answer in terms of the variables given. (15 points)

Explanation / Answer

we will use conservation of energy and conservation of momentum to find the final height'

mgh = 1/2 mu^2

u = velocity with which mass m strikes the heavier mass

gh = 0.5 u^2

u = sqroot ( 2gh)

conserving momentum to find the combined velocity

mu = ( m+ 5m) V

V = ( m/ 6m) sqroot ( 2gh) = 1/6 sq root ( 2gh)

1/2 ( 6m)( 1/6 sq root 2gh) ^2= (6m ) g H---------------conserving energy

1/2 ( 1/36) ( 2gh) = gH

( gh/ 36) = H

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