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A ball with a mass of #5 kg# moving at #8 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

Lily Adams

The velocity of the second ball is #=1.905ms^-1# and the energy lost is #=121.9J#

We have conservation of momentum

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

The mass #m_1=5kg#

The mass #m_2=21kg#

The velocity of the first ball is #u_1=8ms^-1#

The velocity of the second ball is #=v_1ms^-1#

Therefore,

#5*8+21*0=5*0+21*v_2#

#40+0=0+21v_2#

#v_2=40/21=1.905ms^-1#

The kinetic energy before the collision is

#KE_1=1/2m_1u_1^2=1/2*5*8^2=160J#

The kinetic energy after the collision is

#KE_2=1/2m_2v_2^2=1/2*21*(40/21)^2=38.1J#

The energy lost as heat is

#DeltaKE=KE_1-KE_2=160-38.1=121.9J#

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Answer 2

Leo Abeyta

The second ball will move at approximately 2 m/s. The kinetic energy lost as heat in the collision is 176 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.