Work, energy, power and collisions
| English | 中文 | Pinyin |
|---|---|---|
| coefficient of restitution/ˌkəʊɪˈfɪʃənt ɒv rɪstɪˈtjuːʃn/ | 恢复系数 | huī fù xì shù |
What does a slower rebound tell us?
- A ball rebounds slower after hitting a wall. Momentum and kinetic energy answer different parts of the collision story.
- This lesson studies coefficient of restitution 恢复系数: The ratio of relative separation speed to relative approach speed along the line of impact.
Choose the mathematical structure
- Work is force times displacement in its direction. Kinetic energy is mv²/2 and gravitational potential energy is mgh. Momentum is conserved for an isolated collision; restitution gives the relative speed relation, not conservation of kinetic energy.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines coefficient of restitution?
The ratio of relative separation speed to relative approach speed along the line of impact.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A 2 kg particle moving at 6 m/s has kinetic energy 2×6²/2=36 J. If a constant opposing force of 3 N stops it, work=3s=36, giving s=12 m. A wall bounce with approach speed 5 and e=0.6 has rebound speed 3 m/s in the opposite direction.
Work, energy, power and collisions
Work is force times displacement in its direction
Compare the model with the worked case and explain one change.
Find kinetic energy for m=2 kg,v=6 m/s.
Kinetic energy=mv²/2=2×36/2=36 J.
Test a tempting shortcut
- Conserve momentum only when the external impulse is negligible. Kinetic energy is generally lost in an inelastic collision. Power is a rate of energy transfer, not an amount of energy.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
Every collision conserves kinetic energy. This claim is false. Explain which definition or assumption it violates.
A resisting force of 3 N removes 36 J. Find stopping distance.
The resistance removes 3 J per metre: distance=36/3=12 m.
Every collision conserves kinetic energy.
Conserve momentum only when the external impulse is negligible. Kinetic energy is generally lost in an inelastic collision. Power is a rate of energy transfer, not an amount of energy.
Interpret a new situation
- State the direction signs before writing collision equations. For a connected motion problem, choose the whole system for energy when internal tensions cancel; account for frictional work explicitly.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find rebound speed from a wall when approach speed is 5 m/s and e=0.6.
For a fixed wall, rebound speed=e×approach speed=0.6×5=3 m/s.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- edexcel IAL mathematics; official unit M2. Other-unit enrichment is identified in the scope review; it is not an extra cash-in requirement.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The ratio of relative separation speed to relative approach speed along the line of impact. Choose the relationship, show the method, check its assumptions and interpret the result.