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Work is related to force resulting in displacement. However, work holds no relation to the amount of time the force acted to cause the displacement. Sometimes the rate of work done is relatively quick compared to other times when it is slow. Note that the rate of work done is defined as the power.
Let us take an example of work done to climb a rock. A rock climber takes a considerable time to elevate their body to a few meters along a cliff. However, a trail hiker elevates their body to a few meters of the same rock in less time. Though both people did the same work, the hiker took less time than the rock climber.
Thus, the hiker has a better Power rating than the rock climber. The formula for Power determines who took less time to complete the work.
Power Definition
As per the power definition, the rate at which work is done represents the power. Another definition of Power is “the transfer of energy from one place to another or from one form to another in a specific time.”
Work is also considered the transfer of energy, and hence power is also the rate at which energy expends in a particular time. For example, let us consider a 60 W light bulb. It expends 60 J of energy per second.
Great power can be considered as doing a large amount of work or expanding a large amount of energy in short periods. For example, when we accelerate a car rapidly, the vehicle consumes a massive amount of fuel and performs a large amount of work in a short period.
Unit Of Power
The SI Unit of Power is Joules per second and is called Watt in honour of James Watt (1736-1819), a Scottish mechanical engineer. In 1770, he invented improved steam engines and the concept of Power. He introduced Power as the new way of comparing his engines to what they would replace- horses.
Today, motor vehicles’ or machinery’s power is often measured in terms of Horsepower (hp).
According to the British Imperial System, one Horsepower is the power required to lift a mass of 33,000 pounds on one foot in one minute. Thus, one hp equals 33,000 foot-pounds of work in a minute.
In the International System of Unit, the electrical equivalent of 1 hp is 746 watts. The heat equivalent of 1 hp is 2,545 BTU per hour.
Metric Horsepower is another unit of Power. It is equal to 4,500 kg-mtr/m or 0.9863 hp.
Formula for Power
Power is the rate of doing work for a specific period. It is a quantity based on time which further relates to how fast one can do work. Thus, the formula for Power is
Power = Work/time
P = W/t
The expression for work is:
Work = Force x displacement
W = F x d
Power = Force x displacementTime
P = f x dt
Also, expression for velocity is
Velocity = DisplacementTime
V = dt
Therefore, the new formula for Power is,
Power = Force x Velocity
P = f x v
Thus, the new formula for Power tells us that a high power machine is both strong and fast. Consider the following examples:
- Car Engine
- Farm Machinery
- Weightlifter
All these are strong and fast machinery. Thus, the meaning of powers in the giant machine is that it can apply a prominent force for causing displacement in a small amount of time.
Formula For Power in Terms of Force and Velocity
Following is an example of the formula for Power when velocity and force are involved:
- Q) A person applies a force of 10 N and moves the crate 5 m. It took 10 seconds for him to finish this work. What is the Power of this person?
Solution:
Before calculating Power, we need to figure out the work done by the person.
W = Fxd
Substituting the values
W = (10N) x (5m)
W = 50 Nm
Thus, the person did work of 50 Joules.
Now we can determine the Power from the equation
P = Wt
P = 5010js
Therefore P = 5 Js-1
Thus, the person had the Power of 5 Watt.
Conclusion
The power definition states that power is the rate of using energy for a specific period. It also helps in determining the time required to do particular work. It states that the power could change, and hence there are two ways to measure Power. Both methods of measuring power are explained here with an example of using the formula for Power.
