Work, energy and power: average power, slopes and variable resistance
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 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
- Where the fuel goes
- Work done by a force
- Kinds of energy
Read the transcript of the teaching part
Last time
Before we start: last time, in Friction, Newton’s second law and power on a horizontal road, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Where the fuel goes
A car engine burns fuel and the car speeds up. Some of that energy becomes movement. Some is wasted pushing against the air. On a hill, some becomes height. The work-energy equation just keeps the account, and power is how fast the account is being paid.
Work done by a force
Work done is the force times the distance moved in the direction of the force. The unit is the joule. If the force is at an angle to the motion, only its component along the motion counts: F d cosine theta. A force of 40 newtons at 60 degrees to the motion, over 5 metres, does 100 joules of work.
Kinds of energy
Kinetic energy is a half m v squared. Potential energy is m g h. Work done against resistance is resistance times distance. Energy gained is a difference: final minus initial. A car going from 15 to 20 metres per second gains a half m times 20 squared minus 15 squared. For 1400 kilograms that is 280 000 minus 157 500, which is 122 500 joules.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Power on an inclined road.
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.