P = \frac{F \cdot d}{t}

Where:

– P represents Power, which is the rate at which work is done or energy is transferred. Measured in watts (W).

– F represents Force, which is a vector quantity that tends to change the motion of an object. Measured in newtons (N).

– d represents Distance, which is the length traveled by an object in a particular direction. Measured in meters (m).

– t represents Time, which is the duration in which work is done. Measured in seconds (s).

Power is defined as the rate at which work is done or energy is transferred. It is a fundamental concept in physics and is denoted by the symbol P. Power can be calculated using the formula:

P = \frac{W}{t}

where **P** is the power, **W** is the work done, and t is the time taken to do the work. The unit of power is the watt (W), which is equivalent to one joule per second.

One common experiment to measure power is the lifting of a mass against gravity. By measuring the time taken to lift a mass to a certain height, the work done can be calculated. From this, power can be determined using the formula mentioned above.

In the past, various practical applications have been developed to substantiate the concept of power. For example, in the field of mechanical engineering, the power output of an engine is a critical parameter in designing and optimizing machines. The power generated by a motor can also be measured experimentally using a dynamometer.

Power can also be derived from the equation for work done. Work is defined as the force applied over a distance, which can be expressed as:

W = F \cdot d

Substituting this into the formula for power, we get:

P = \frac{F \cdot d}{t}

Power is closely related to energy, as energy is the ability to do work. The rate at which energy is transferred or converted is equal to power. Therefore, power can also be calculated using the equation:

P = \frac{E}{t}

where E is the energy transferred. This equation shows that power is the rate at which energy is transferred over time.

Power is an essential concept in physics that quantifies the rate at which work is done or energy is transferred. It can be calculated using various formulas, including those derived from work and energy equations. Practical applications and experiments have been conducted in the past to substantiate the concept of power in different fields of physics and engineering.

Continue Reading Note on Power
It Sticks!

Power

P = 50W

t = 4 hours

E = P \times t

E = 50W \times 4 hours

E = 200 Wh

Therefore, the machine consumes 200 watt-hours of energy.

P = 2.5 kW

t = 3 hours

W = P \times t

W = 2.5 kW \times 3 hours

W = 7.5 kWh

The motor has done 7.5 kilowatt-hours of work.

P = 60W

t = 8 hours

E = P \times t

E = 60W \times 8 hours

E = 480 Wh

The light bulb consumes 480 watt-hours of energy.

E = 500 J

t = 10 seconds

P = \frac{E}{t}

P = \frac{500 J}{10 seconds}

P = 50W

The power rating of the device is 50 watts.

P = 1500W

t = 20 minutes = \frac{20}{60} hours = \frac{1}{3} hours

E = P \times t

E = 1500W \times \frac{1}{3} hours

E = 500 Wh

The electric kettle consumes 500 watt-hours of energy when used for 20 minutes.

More Worked Examples on Power
It Sticks!

1. What is the formula for power in physics when work is done over a certain amount of time?**A:** P = \frac{W}{t}

2. If a force of 10 N is applied to an object and it moves a distance of 5 meters in 2 seconds, what is the power output?**A:** P = \frac{W}{t} = \frac{Fd}{t} = \frac{(10)(5)}{2} = 25 \text{ watts}

3. A motor produces 500 J of work in 10 seconds. What is the power output of the motor?**A:** P = \frac{W}{t} = \frac{500}{10} = 50 \text{ watts}

4. A light bulb consumes 60 watts of power. How much work does it do in 5 seconds?**A:** P = \frac{W}{t} \rightarrow W = Pt = (60)(5) = 300 \text{ joules}

5. A power plant generates 1000 MW (megawatts) of power. How much energy does it produce in 1 hour?**A:** P = \frac{W}{t} \rightarrow W = Pt = (1000)(1 \text{ hour}) = 1000 \text{ MWh}

6. A car engine has a power output of 150 hp (horsepower). How long would it take for the engine to do 3000 J of work?**A:** P = \frac{W}{t} \rightarrow t = \frac{W}{P} = \frac{3000}{150} = 20 \text{ seconds}

7. A motorbike engine produces 40 N of thrust and moves at a speed of 10 m/s. What is the power output of the engine?**A:** P = Fv = (40)(10) = 400 \text{ watts}

8. A wind turbine generates 2 MW of power. How much work is done in 1 hour?**A:** P = \frac{W}{t} \rightarrow W = Pt = (2)(1 \text{ hour}) = 2 \text{ MWh}

9. If a force of 15 N is applied to push a box 5 meters in 3 seconds, what is the power output?**A:** P = \frac{W}{t} = \frac{Fd}{t} = \frac{(15)(5)}{3} = 25 \text{ watts}

10. A hydroelectric dam produces 500 MW of power. How much work does it do in 1 minute?**A:** P = \frac{W}{t} \rightarrow W = Pt = (500)(1 \text{ minute}) = \frac{500}{60} \text{ MWh}

11. A rock climber lifts a 50 kg rock to a height of 20 meters in 10 seconds. What is the power output?**A:** P = \frac{W}{t} = \frac{mgh}{t} = \frac{(50)(9.8)(20)}{10} = 980 \text{ watts}

12. A light bulb uses 30 J of energy in 5 seconds. What is the power consumption of the light bulb?**A:** P = \frac{W}{t} = \frac{30}{5} = 6 \text{ watts}

13. A jet engine produces 30 kN of thrust and moves at a speed of 100 m/s. What is the power output of the engine?**A:** P = Fv = (30)(100) = 3000 \text{ watts or 3 kW}

14. A solar panel generates 500 W of power. How much energy does it produce in 1 hour?**A:** P = \frac{W}{t} \rightarrow W = Pt = (500)(1 \text{ hour}) = 500 \text{ Wh}

15. A water pump does 1000 J of work in 20 seconds. What is the power output of the pump?**A:** P = \frac{W}{t} = \frac{1000}{20} = 50 \text{ watts}

Â

Quick Answers for Power
It Sticks!