Question

In a ballistic pendulum experiment, a small marble is fired into a cup attached to the end of a pendulum. If the mass of the marble is 0.0295 kg 0.0295 kg and the mass of the pendulum is 0.250 kg 0.250 kg , how high will the pendulum swing if the marble has an initial speed of 5.45 m/s 5.45 m/s ? Assume that the mass of the pendulum is concentrated at its end so that linear momentum is conserved during this collision.

Answer 1

1. To determine the initial momentum
Initial momentum = 0.0295 x 5.45 = 0.16 kgm/sec or Nsec
Final momentum = (0.0295 + 0.250) x v = 0.2795 x v
0.2795 * v = 0.16
v = 0.572 m/s

The pendulum will swing until the angular velocity of the zero. At this position,

the total kinetic energy is zero.

To determine the kinetic energy:
KE = ½ x 0.2795 x(0.572)² = 0.0457J
To determine the maximum height, set the total final potential energy equal to the initial kinetic energy.
PE = 0.2795 * 9.8 * h = 2.74 * h
2.74 * h =0.0457
h = 0.017 meter
This is approximately 0.017 meter or 1.7 cm above the lowest position of the bottom of the pendulum.