A ball with a mass of 0.3 kg hangs from a string forming a pendulum. The pendulu

Question

A ball with a mass of 0.3 kg hangs from a string forming a pendulum. The pendulum is allowed to swing, starting from rest at a height of 1.3 m, and collide with a 0.5 kg cart initially at rest. After the collision the cart rolls up a ramp rising to a height of 0.25 m and the ball swings back rising to a height of 0.5 m. a) Determine the initial mechanical energy of the system consisting of the ball and the cart. b) How much energy has been converted to non-mechanical form due to the collision and any friction that acts? c) If instead all the energy gained by the cart remains in mechanical form how high up the ramp will the cart rise? Assume the energy transfer during the collision is unchanged.

A ball with a mass of 0.3 kg hangs from a string forming a pendulum. The pendulum is allowed to swing, starting from rest at a height of 1.3 m, and collide with a 0.5 kg cart initially at rest. After the collision the cart rolls up a ramp rising to a height of 0.25 m and the ball swings back rising to a height of 0.5 m. Determine the initial mechanical energy of the system consisting of the ball and the cart. How much energy has been converted to non-mechanical form due to the collision and any friction that acts? If instead all the energy gained by the cart remains in mechanical form how high up the ramp will the cart rise? Assume the energy transfer during the collision is unchanged.

Explanation / Answer

a) initial mechanical energy of the system = pot energy of pendulum = 0.3*9.8*1.3 = 3.822 J

b) final mechanical energy = pot energy of cart + pot energy of pendulum

= 0.5*9.8*0.25 + 0.3*9.8*0.5 = 2.695 J

so energy that has been converted to non-mechanical form due to the collision and any friction that act = intial energy - final

= 3.822 - 2.695 = 1.127 J

c) Final energy of pendulum = 0.3*9.8*0.5 = 1.47 J

so final energy of cart = 3.822 - 1.47 = 2.352 J

so 0.5*9.8* h = 2.352

so height = 0.48 m

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