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

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

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