A student performs a ballistic pendulum experiment using an apparatus similar to

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 cm,
at the maximum height the pendulum sub-
tends an angle of 42.8 degrees,
the mass of the bullet is 75 g, and
the mass of the pendulum bob is 819 g.
The acceleration of gravity is 9.8 m/s2 .
Determine the initial speed of the projec-
tile.
Answer in units of m/s.

Explanation / Answer

Given that mass of bullet m = 75 x 10^-3 kg mass of block M = 0.819 kg Maximum height h = 0.04 m acceleration due to gravity g =9.80 m/s2 ---------------------------------------------------------- Using the conservation of mechanical energy after the collision, we relate the post collision speed vf to the maximum height h:          (1/2)(m+ M)vf^2 = (m + M)gh                     vf = (2gh) Using conservation of momentum during the collision we related velocities v1i and vf:       mv1i = (m+ M)vf So the initial speed of the projectile is          v1i =[ (m+ M)/m]  (2gh)                = [( (75 x 10^-3 kg) +( 0.819 kg))/( 75 x 10^-3 kg)][2(9.80 m/s2)(0.04 m)]                = 10.55 m/s

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