Work and energy on slopes, with an engine and with friction
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Energy instead of forces
- The energy equation
- A smooth plane
Read the transcript of the teaching part
Last time
Before we start: last time, in Work and energy on curves, connected particles and rough planes, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Energy instead of forces
You could solve a slope problem with forces and suvat. But when the question says use an energy method, you only need three things: kinetic energy, potential energy, and work done by forces that are not gravity. Add what goes in, subtract what is lost, and there is no need for the acceleration at all.
The energy equation
Kinetic energy is half m v squared. Potential energy gained is m g times the vertical height gained. The work-energy principle says: initial energy, plus work done by the engine, equals final energy, plus work done against resistance. On a slope, the vertical height is the distance along the plane times sine of the angle.
A smooth plane
A particle of mass 0.6 is projected at 4 down a smooth plane inclined at 10 degrees. After 15 metres, the vertical drop is 15 sine 10. Initial KE: half times 0.6 times 16, which is 4.8. PE lost: 0.6 times 10 times 15 sine 10, which is 15.63. Energy: 4.8 plus 15.63 equals half times 0.6 times v squared. So v squared is 68.1 and v is 8.25.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Work–energy on an inclined plane · Work–energy with friction.
The whole chapter: Energy, Work and Power.
Chapter 4.5: Energy, work and power
- Friction, Newton’s second law and power on a horizontal road 6 min
- Work, energy and power: average power, slopes and variable resistance 6 min
- Work and energy on curves, connected particles and rough planes 6 min
- Work and energy on slopes, with an engine and with friction 6 min
Also for A Level Maths 9709 Paper 4
Which topics come up most in A Level Maths 9709 Paper 4 past papers, counted from every paper since 2004.