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A ball with a mass of #9 kg# moving at #3 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?

Answer 1

Use conservation of momentum and conservation of energy
#v_2' = 9/21 3 = 9/7 m/s#
energy lost to collision = 40.5-17.36 = 23.14 J

Momentum of the system before collision: #m_1v_1 + m_2v_2 = m_1v_1'+ m_2v_2' # #m_1 = 9 kg; m_2 = 21 kg; v_1 = 3 m/s; v_2 = 0; v_1' = 0# #v_2' = m_1/m_2v_1# substitute #v_2' = 9/21 3 = 9/7 m/s# now kinetic energy before #KE = 1/2mv^2; KE_i = 1/2 9 (3)^2 ; KE_f = 1/2 21 (9/7)^2 # #KE_i = 1/2 9*9 = 40.5 J; KE_f = 1/2 3 (9)^2/7 = 17.36 J # energy lost to collision = 40.5-17.36 = 23.14 J

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Answer 2

Isabella Alvarez

The second ball will move at 1 m/s. The kinetic energy lost as heat in the collision is 36 J.

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Answer from HIX Tutor

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.