Question

Two 0.75m -long pendulums hang side by side. The masses of the pendulum bobs are 65g and 85g . The lighter bob is pulled aside until its string is horizontal and is then released from rest. It swings down and collides elastically with the other bob at the bottom of its arc.To what height does the lighter bob rebound?

Answer 1

momentum is conserved, energy is conserved in an elastic collision.

first pendulum:
m g h= at the bottom 1/2 m v^2

v= sqrt (2g*.75) that is velocity of m1 at the bottom. solve for v

Now, the collision
momentum:
.065*v=.065v'+.085v2
energy:
1/2 .065v'^2=1/2 .065v'^2+ 1/2 .085 v2^2

so in those , you have two unknowns v' and v2
two equations, two unknowns. Solve for v' in the first equation, put it in the second equation, and solve for v2. Have a blank pad with lots of room to do the agebra.
Now, knowing v2, the height it goes:
1/2 .085 v2^2= .085 h * g
solve for h.