A 2.5 kg wood block hangs from the bottom of a 1.0 kg, 1.2 m long rod. The block and rod form a pendulum that swings on a frictionless pivot at the top end of the rod. A 12 g bullet is fired into the block, where it sticks, causing the pendulum to swing out to a 33 angle.
The Attempt at a Solution
Since the kinetic energy of the bullet all ends up as potential energy at the top of the swing I set kinetic energy equal to the sum of all the gravitational potential energies. The height that the rod goes would be from its center of mass so it would be cos33=h/.6 which equals .5m. Then the height of the bullet and the block would be cos33=h/1.2 which equals 1 m. Then I used the equation 1/2mv2= mgh + (m+m)gh and that plugged in with numbers looks like 1/2(.012)v2=1(9.81)(.5) +(2.5 +.012)(9.81)(1) and then I solved for v and got v= 70.2 m/s
I do not know where I went wrong. If anybody could help me that would be great and I would really appreciate it.