1. Before
After
351 m/s
What is the KE before and after?
0.012 kg
3.215 kg

2. Before
After
351 m/s
To what height does the pendulum rise?
0.012 kg
3.215 kg

3. So the bullet will impart its momentum to the block:
(0.012 kg)(351 m/s) = (0.012 kg kg)(v)
v = m/s
Now energy will be conserved as it swings like a pendulum:
1/2mv2 = mgh
1/2v2 = gh
1/2(1.305 m/s)2 = (9.81 N/kg)h
h = m

4. Before After Δh = .042 m v = ? .0065 kg 3.215 kg
Find the initial velocity of the bullet before it hits the block.
.0065 kg
3.215 kg
450 m/s

5. To rise .042 m, the bullet and block must have had this velocity:
1/2mv2 = mgh
1/2v2 = gh
1/2v2 = (9.81 N/kg)(.042 m)
v = m/s
Work backwards using COM:
(.0065 kg)v = ( kg)( m/s)
v = m/s ≈ 450 m/s

6. How high above its original position will the block of wood fly?
1.150 kg
.0062 kg
v = 673 m/s
.66 m

7. So the bullet will impart its momentum to the block:
( kg)(673 m/s) = ( kg kg)(v)
v = m/s
Now energy will be conserved as it flies up in the air:
1/2mv2 = mgh
1/2v2 = gh
1/2(3.609 m/s)2 = (9.81 N/kg)h
h = 0.66 m