Signed velocities and energy in a collision
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Momentum and impulse. Read the relevant method, then decide which parts you can solve without hints.
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Particles of masses 3 kg and 1 kg approach one another on a line. The positive axis points from the first towards the second before impact. Their signed velocities are 4 and -2 m/s respectively. The coefficient of restitution is and external impulse is negligible.
Part a
Find their final signed velocities, in particle order.
Part b
Find the loss of kinetic energy in joules.
Part c
Interpret the directions after impact and check that the particles separate.
Model solution and review criteria
Part a
Conserve momentum: 3V+1W=10. Restitution gives W−V=(4−(-2))/2=3. Solving gives V=, W=.
- Use signed velocities in momentum.
- Use separation speed relative to approach speed.
- Solve the two equations.
Part b
Initial energy is (52)/2. Final energy is (3()²+1()²)/2. Their difference is J.
- Use squares of velocities, not signed kinetic energies.
- Subtract final energy from initial energy.
Part c
The sign of V= gives the first direction; W=>V gives positive relative separation speed 3. A negative final velocity is a direction, not a negative speed or energy.
- Interpret signs individually.
- Use W−V to establish separation.
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