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CIE A-Level Maths Study Notes

3.5.4 Power and Its Calculations

Power is a central concept in physics, representing the rate of work done or energy transfer. Understanding power helps explain how systems evolve under various forces.

Power: Definition and Formula

  • Power measures the rate of work or energy use per time. It's calculated as: P=WtP = \frac{W}{t}

Power in Relation to Force and Velocity

  • Power is also calculated by multiplying force FF by velocity vv: P=F×v P = F \times v
Force-Velocity Relationship

Image courtesy of Wikipedia

Calculating Power

  • Rate of work: P=WtP = \frac{W}{t}
  • Using force and velocity: P=F×vP = F \times v

Examples of Power Calculation

Example 1: Lifting a Weight

Scenario: Lifting a 20 kg weight to a height of 2 meters in 4 seconds. Calculate the force, work done, and power.

Solution:

1. Force due to Gravity:

  • F=mg=20×9.8=196NF = mg = 20 \times 9.8 = 196 \, \text{N}

2. Work Done:

  • W=F×h=196×2=392JW = F \times h = 196 \times 2 = 392 \, \text{J}

3. Power:

  • P=Wt=3924=98WattsP = \frac{W}{t} = \frac{392}{4} = 98 \, \text{Watts}

4. Conclusion: The power required to lift the weight is 98 Watts.

Example 2: Car Moving at Constant Velocity

Scenario: Calculate the power for a car moving at 25 m/s under a force of 500 N.

Solution:

1. Calculating Power:

  • Power formula for constant velocity: P=F×vP = F \times v
    • Where F=500N)and(v=25m/sF = 500 \, \text{N}) and (v = 25 \, \text{m/s}
  • Calculation: P=500×25=12500WattsP = 500 \times 25 = 12500 \, \text{Watts}

2. Conclusion: A car moving at 25 m/s under a force of 500 N exerts 12500 Watts of power.

Dr Rahil Sachak-Patwa avatar
Written by: Dr Rahil Sachak-Patwa
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Oxford University - PhD Mathematics

Rahil spent ten years working as private tutor, teaching students for GCSEs, A-Levels, and university admissions. During his PhD he published papers on modelling infectious disease epidemics and was a tutor to undergraduate and masters students for mathematics courses.

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