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A ball with a mass of #6 kg# moving at #1 m/s# hits a still ball with a mass of #24 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

Julia Aguilar

The second ball moves at 0.25 m/s. The kinetic energy lost as heat in the collision is 18.5 J.

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Answer 2

Benjamin Asiedu

The kinetic energy lost as heat in the collision is #=2.25J#

We have conservation of momentum

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

The mass the first ball is #m_1=6kg#

The velocity of the first ball before the collision is #u_1=1ms^-1#

The mass of the second ball is #m_2=24kg#

The velocity of the second ball before the collision is #u_2=0ms^-1#

The velocity of the first ball after the collision is #v_1=0ms^-1#

Therefore,

#6*1+24*0=6*0+24*v_2#

#24v_2=6#

#v_2=6/24=0.25ms^-1#

The velocity of the second ball after the collision is #v_2=0.25ms^-1#

The loss in kinetic energy is

#DeltaKE=KE_i-KE_f#

#=1/2*6*1^2-1/2*24*0.25^2#

#=3-0.75#

#=2.25J#

The kinetic energy lost as heat in the collision is #=2.25J#

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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.