A ball with a mass of #2 kg# moving at #16 m/s# hits a still ball with a mass of #21 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?
In the first scenario, momentum conservation law will be applied.
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To find the velocity of the second ball after the collision:
v2_final = (m1 * v1_initial) / m2 v2_final = (2 kg * 16 m/s) / 21 kg v2_final ≈ 1.5238 m/s
To find the kinetic energy lost as heat in the collision:
Initial kinetic energy: KE_initial = 0.5 * m1 * v1_initial^2 + 0.5 * m2 * v2_initial^2 KE_initial = 0.5 * 2 kg * (16 m/s)^2 + 0.5 * 21 kg * (0 m/s)^2 KE_initial = 256 J + 0 J KE_initial = 256 J
Final kinetic energy: KE_final = 0.5 * m1 * v1_final^2 + 0.5 * m2 * v2_final^2 KE_final = 0.5 * 2 kg * (0 m/s)^2 + 0.5 * 21 kg * (1.5238 m/s)^2 KE_final = 0 J + 23.0664 J KE_final ≈ 23.0664 J
Kinetic energy lost = 256 J - 23.0664 J Kinetic energy lost ≈ 232.9336 J
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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