Q227 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 227 (5 marks)
On a frictionless arcade track, a 2 kg cart moves right at 6 m/s and a 1 kg cart moves left at 3 m/s. They collide and remain joined. External impulse is negligible.
a)[2 marks]
Find their common velocity immediately after collision.
b)[3 marks]
Find kinetic energy lost and explain why momentum conservation does not imply energy conservation.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) m/s rightwards. (b) J lost.
Worked solution
(a) With right positive, momentum is 2(6)+1(-3)=9 kg m/s. The combined mass is 3 kg, giving common velocity 9/3=3 rightwards.
(b) Initial kinetic energy is J. Final kinetic energy is J. Loss is 27 J. Momentum is conserved with negligible external impulse; this inelastic collision converts kinetic energy to other forms.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Part a: Use signed initial momentum.
Part a: Calculate and interpret common velocity.
Part b: Find initial energy.
Part b: Find final energy and loss.
Part b: Explain the distinction between conserved momentum and kinetic energy.
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