Work and Energy


Let us consider a situation wherein a rock climber takes an abnormally long time in order to elevate her body up a few meters along the cliff. Whereas a hiker who takes the easier path up the cliff elevates her body a few meters in a short amount of time. Both of the people do the same amount of work, yet the hiker does the work in less time than the rock climber. The hiker has a greater power than the rock climber. But what is the power?  How do we determine it? Let us study more about it below.

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What is the Power?

It is the rate of doing work or the rate at which energy transfers in a unit of time. It increases if work is done faster or the energy transfer occurs in less time.

Mathematically, power (P) = W/ t, where

  • P = power (in watts)
  • W = the amount of work done or energy
  • t = time (in seconds)

Since, Work (W) = Force (F) * Displacement (d)  and Velocity (v) = Displacement (d) / Time (t), therefore

Power (P) = Force (F) * Velocity (v)

It is more when the system is both strong in force and fast in velocity.

the power

Power Unit

Its measurement occurs in energy (joules) divided by time. Its SI unit is watt (W) or joule per second (J/s). It is a scalar quantity and has no direction. Often to describe the power by machine ‘Horsepower’ is used.

Watt is seen in relation to light bulbs. Here, it is the rate at which the bulb converts electrical energy into light and heat. Usage of electricity per unit of time is more if there’s a bulb with a higher wattage.

When we know the power of a system, we can find the amount of work done, i.e. W=Pt.

Work and Power

When you walk some distance, it is measured as the work done since your motive force is displacing your body.Whereas when you are running the same mile, you are doing the same amount of work but the time taken is less. A runner has a higher power than the walker, putting out more wattage.

Average Power

When discussing power, people usually refer to average power, Pavg. It is the amount of work done in a period of time (ΔW/Δt) or the amount of energy transfer occurring in a period of time (ΔE/Δt).

Instantaneous Power

When a unit of time approaches zero, it is approximated by force times speed.

Solved Example For You

Q. Which of the following must be known in order to determine the power output of an automobile?

a. Final velocity and height

b. Mass and amount of work performed

c. Force exerted and distance of motion

d. Work performed and elapsed time of work

Sol: d. Work performed and elapsed time of work

Power is defined as the rate of doing work. For the automobile, the power output is the amount of work done (overcoming friction) divided by the length of time in which the work was done.

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