Question

A student performs a ballistic pendulum experiment using an apparatus similar to that shown in the figure.
Initially the bullet is fired at the block while the block is at rest (at its lowest swing point). After the bullet hits the block, the block rises to its highest position, see dashed block in the figure, and continues swinging back and forth.
The following data is obtained:
the maximum height the pendulum rises is 4.5 cm,
the mass of the bullet is 82 g, and
the mass of the pendulum bob is 863 kg.
Find the final velocity of the system (m1 + m2) immediately after the collision and before the pendulum starts to swing upward. The acceleration of gravity is 9.8 m/s2 .
Answer in units of m/s

Answer 1

mass of system = M = .082 + 863

Kinetic energy at bottom = potential energy at top

(1/2) M v^2 = M g (.045)
or
v^2 = 2 (9.8)(.045)

solve for v, total velocity at bottom after collision
note - the masses do not matter

Answer 2

.939