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 0.0285 kg and the mass of the pendulum is 0.250 kg , how high will the pendulum swing if the marble has an initial speed of 5.35 m/s ? Assume that the mass of the pendulum is concentrated at its end so that linear momentum is conserved during this collision.

h = 0.015 m

Explanation:

m = mass of the marble = 0.0285 kg

M = mass of the pendulum = 0.250 kg

v = initial velocity of the marble before collision = 5.35 m/s

V = final velocity of marble-pendulum combination after the collision = ?

using conservation of momentum

m v = (m + M) V

(0.0285) (5.35) = (0.0285 + 0.250) V

V = 0.548 m/s

h = height gained by the marble-pendulum combination

Using conservation of energy

Potential energy gained by the combination = Kinetic energy of the combination just after collision

(m + M) gh = (0.5) (m + M) V²

gh = (0.5) V²

(9.8) h = (0.5) (0.548)²

h = 0.015 m