Lesson 8, Topic 3
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# Power

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Power is defined as time rate of doing work. It is measured in Watt or Js-1.

Power =  $$\frac {work-done}{time} \scriptsize = \normalsize \frac {j}{s}$$

Power = $$\frac {force \: \times \: distance}{time}\scriptsize = \normalsize \frac {j}{s}$$

P $$\scriptsize = Force \: \times \: \normalsize \frac {distance}{time}$$

Velocity = $$\frac {distance}{time}$$

P = Force x Velocity

= FV (Nms-1)

From the deduction, power can also be calculated by Force x Velocity.

Units of Power:

• Watt
• Joule per second J/s
• Newton meter per second Nm/s
• Kilogram meter per the second cube Kgm/s³

Example

i. A boy lifts a mass of 50kg vertically through a height of 3m in 20seconds. Calculate the power developed.

Solution

Values given:

mass = 50kg, height = 3m

t = 20 seconds

Power =  $$\frac {work-done}{time}$$

But work done = mgh = 50 x 10 x 3

=  $$\frac {50 \: \times \: 10 \: \times \: 3}{20}$$

=  $$\frac {1500}{20}$$

= 75 Watt

ii.  A force of 30N acts on a 0.5kg mass for 2 minutes. If the distance moved by the mass is 400cm,

calculate

(a) the power generated by the force.

(b) the acceleration of the object.

(c) its velocity.

Solution

Values Given:

Mass = 0.5kg, force = 30N

time = 2 minutes = 2 x 60 seconds = 120 seconds

distance = 400 cm = 400 / 100 = 4 m

(a) Power = $$\frac {work-done}{time}$$

Power = $$\frac {force \: \times \: distance}{time}$$

Power = $$\frac {30N \: \times \: 4m}{120}$$

Power = $$\frac {120}{120}$$

Power = 1 Watt

(b) To calculate the acceleration of the object, you use the formula,

Force = mass x acceleration.

30 = 0.5 x acceleration.

Make acceleration the subject of the formula

acceleration = $$\frac {30}{0.5}$$

∴ acceleration = 60ms-2

(c) To calculate the velocity

use the formula

Power = force x velocity

velocity = $$\frac{Power}{force} = \frac{1}{30} \\ = \scriptsize 0.033 m/s$$ error: