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: $P = \frac{W}{t}$

Power in Relation to Force and Velocity

• Power is also calculated by multiplying force $F$ by velocity $v$: $P = F \times v$

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Calculating Power

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

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:

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

2. Work Done:

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

3. Power:

• $P = \frac{W}{t} = \frac{392}{4} = 98 \, \text{Watts}$

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: $P = F \times v$
  • Where $F = 500 \, \text{N}) and (v = 25 \, \text{m/s}$
• Calculation: $P = 500 \times 25 = 12500 \, \text{Watts}$

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