A 5.00-g bullet is fired into a 950-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 8.00 cm.What was the kinetic energy of the bullet immediately before the collision?
A)1.4E+2 J
B)1.5E+3 kJ
C)3.9E-3 J
D)1.4E+8 J
E)1.5E+2 J

Question

Quizplus · Accepted Answer

Using conservation of momentum and conservation of energy, we can solve for the initial kinetic energy of the bullet:
momentum before = momentum after
mv = (m+M)V
where v is the initial velocity of the bullet, M is the mass of the block, and V is the velocity of the combined mass after the collision. Rearranging, we get:
v = (M/m+M)V
Next, using conservation of energy, we have:
KE before = KE after
1/2mv^2 = (m+M)gh
where h is the height the combined mass swings to. Substituting for v and solving for KE before, we get:
KE before = 1/2(m+M)V^2 = 1/2(m+M)(h(g/(M+m)))^2 = 1.4x10^2 J. Therefore, the answer is (A).

A 500-G Bullet Is Fired into a 950-G Block of Wood