Inelastic Collision and Pendulums

[seichan]

Homework Statement

Two 23-cm long pendulums (each made of a massless string and a ball) are initially situated as shown in the figure. The masses of the left and right balls are m1= .145 kg and m2= .200 kg , respectively. The first pendulum is released from a height d= .092 m and strikes the second. Assuming that the collision is completely inelastic and neglecting the mass of the strings and any frictional effects, how high does the center of mass rises after the collision?

Homework Equations

U(x)=mgh
KE=1/2mv^2

The Attempt at a Solution

I started out by solving for the velocity of mass one when it strikes mass two. Because it is raised to a height d, its potential energy is mgd. Because energy is conserved, this is equal to the kinetic energy at its equilibrium point (where mass two is at rest). Thus, m1gd=.5m1V^2
sqrt(2gd)=V
I then used this velocity to calculate the Kinetic energy of mass two.
.5m2V^2=KE
.5m2(2gd)=KE
m2gd=KE
This, in turn, is equal to the potential energy at the height it goes to. Thus:
m2gh=m2gd
h=d

This, however is not the case (clearly). Whatever you could tell me about where my thinking has gone wrong would be greatly appreciated.

 

[Shooting Star]

[

The Attempt at a Solution

I started out by solving for the velocity of mass one when it strikes mass two. Because it is raised to a height d, its potential energy is mgd. Because energy is conserved, this is equal to the kinetic energy at its equilibrium point (where mass two is at rest).

It is mentioned explicitly that the collision is completely inelastic. In such collisions, mechanical energy is not conserved, and the two objects stick together. But the momentum of the system just before collision is equal to the momentum just afterward. From that you can find the speed just after impact.

Try it now.

 

[Dick]

The problem says that the collision is completely inelastic. This means that the bodies stick together after the collision. This means that V of m1 is NOT equal V of m2 after the collision. Use conservation of momentum to find the velocity of the combined mass after the collision and then figure how high it goes.