16.0.0: WORK AND POWER

16.0.0: WORK AND POWES
16.1.0: WORK:
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.

UNIT OF WORK:
The s.I. unit of work is joule.work can also be measured in other units which is NewtonMeter ( Nm)

FORMULA FOR CALCULATING WORK DONE:
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

APPLICATION OF FORMULA:
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


16.2.0: 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.

UNIT OF POWER:
The s.I. unit of power is Watt. It can be calculated in other units such as joule per second and so on.

OTHER UNITS OF POWER:

• joule per second J/s
• Newton meter per second Nm/s
• Kilogram  meter per second cube Kgm/s³

FORMULA FOR CALCULATING POWER:

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

APPLICATION OF FORMULA:

EXAMPLES:

1.   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.

SOULTION:

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