Views: 51
Work and Power
work is done when a force moved an object through a distance in the direction of the force. It is also the product of a force that act on an object and the distance moved by the object in the direction of the force.
The s.I. unit of work is joule.work can also be measured in other units which is Newtonmeter ( Nm)
Word Done = force x distance moved in the direction of force.
Work Done = F x S
Recall that F = m x a,
Therefore, we can write,
Work Done = mass x acceleration x distance
Examples:
1. Calculate the amount of work that is done when a force of 25 N move 10 kg mass through a distance of 1.25 m.
Solution:
Data given in the question:
Force = 25 N, distance = 1.25 m, mass = 10kg
Formula : Work Done = Force x distance
Substitution: Work Done = 25N x 1.25 m.
2. If the work done by a force on an object is 25.3J and the distance moved by the object is 1.23m, calculate the amount of the force that was applied on the object.
Solution:
Data given in the question:
Work Done = 25.3J, distance = 1.23m
Formula : Work Done = Force x distance
Substitution: 25.3 = Force x 1.23m
Make Force the subject of the formula,
Force = 25.3 / 1.23 .
Force = 20.57 N
Power:
Power is the time rate of work done by a force. It is the ratio of work done to time taken to do the work.
The s.I. unit of power is Watt. It can be calculated in other units such as joule per second ,Newton meter per second Nm/s Or Kilogram meter per second cube Kgm/s³
- Power = Work Done / time taken
- Remember that Work done = force x distance
Therefore,
- Power = force x distance / time,
- Also, remember that force = mass x acceleration,
then
- Power = ( mass x acceleration x distance ) / time.
- Also, remember that acceleration = velocity / time, then,
- Power = ( mass x ( velocity / time ) x distance ) / time.
- Also, remember that,
- Velocity = distance / time.
Then,
- Power = ( mass x (( distance / time )/ time ) x distance ) / time.
- Therefore, Power = ( mass x distance² ) / time³
Examples:
- A force of 15N act on 0.5kg mass for 2 minutes. If the distance moved by the mass is 200cm, calculate the the power generated by the force, the acceleration of the object and its velocity.
Solution:
Data given in the question:
- Mass = 0.5kg, force = 15N, time = 2 minutes = 2 x 60 seconds = 120 seconds,
- distance = 200 cm = 200 / 100 = 2 m
- Formula : Power = work done / time.
- Power = force x distance / time
- Substitution : Power = 15 x 2 / 120.
- Power = 0.25 Watt.
To calculate the acceleration of the object, you use the formula,
Force = mass x acceleration.
- 15 = 0.5 x acceleration. Then you make acceleration subject of the formula, then,
- acceleration = 15 / 0.5
- acceleration = 30 m/s²
- To calculate the velocity of the object, you use the formula,
- Acceleration = velocity / time.
- Substitution : 30 m/s² = velocity / 120 seconds.
- Make Velocity the subject, then,
- Velocity = 30 m/s² X 120 seconds
- Velocity = 3600 m/s