Question

A ballistic pendulum consists of a thin rod AB (length = 2.0 m; mass = 1.14 kg) that is rigidly attached to a solid sphere that has a center C, radius = 0.4 m, and mass = 2.45 kg. A bullet (mass = 0.01 kg) is fired at point C with a speed of 675 m/s.
Determine the amount of kinetic energy lost by the system due to the impact.

Answer 1

the ratio of the mechanical energy after the collision to the mechanical energy before the collision is equal to the ratio of the kinetic energy of the ballistic pendulum+ bullet immediately after the collision to the kinetic energy of the bullet before the collision.

Ef Ei

=

½ (m+M)vf2 ½ mvo2

=

(m+M)vf * vf mvo * vo

From conservation of momentum we know that (m+M)v_f = mv_o, so:

Ef Ei

=

vf vo

=

m m + M

In the numerical we had m = 0.01kg g and M = 3.59kg, so E_i/E_f = 0.003.
0.3% of the kinetic energy remains - in other words, 99.7% was lost or transformed into other forms of energy (mostly thermal energy)