# A ball with a mass of #14 kg# moving at #15 m/s# hits a still ball with a mass of #17 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

The entirety of linear momentum is always conserved in both directions, according to the Principle of Conservation of Linear Momentum.

Utilizing the linear momentum conservation principle:

Since kinetic energy is not conserved, this energy is lost from the mechanical system and transformed into other forms of energy, such as heat, which is why the collision is referred to as inelastic.

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To find the velocity of the second ball after the collision, you can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Total momentum before collision = Total momentum after collision

(14 kg * 15 m/s) = (14 kg * 0 m/s) + (17 kg * v2)

Solving for v2:

14 kg * 15 m/s = 17 kg * v2 v2 = (14 kg * 15 m/s) / 17 kg v2 ≈ 12.35 m/s

To find the kinetic energy lost as heat in the collision, you need to calculate the initial kinetic energy and the final kinetic energy, then find the difference.

Initial kinetic energy (KE_initial) = (1/2) * mass * velocity^2 KE_initial = (1/2) * 14 kg * (15 m/s)^2 KE_initial ≈ 1575 J

Final kinetic energy (KE_final) = (1/2) * mass * velocity^2 KE_final = (1/2) * 17 kg * (12.35 m/s)^2 KE_final ≈ 1070.82 J

Kinetic energy lost as heat = KE_initial - KE_final Kinetic energy lost as heat ≈ 1575 J - 1070.82 J Kinetic energy lost as heat ≈ 504.18 J

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