When an object is dropped from above the ground, work is done as the object is pulled to the ground. As the object is falling and work is done, the potential energy of the body is changed to kinetic energy. In principle, the quantity of potential energy stored in a body is always equal to kinetic energy produced when the body is released to do work. In other words, when energy changes, for example from potential to kinetic, there is always an accompanying work done.
EXAMPLE
What work is done when a mass of 6kg is raised through a vertical height of 3.5m(acceleration due to gravity is 10m/s2)
Mass=6kg
Acceleration (due to gravity) =10m/s2
Workdone W=Mass x acceleration x distance
= 6kgx10x 3.5
=210 joules.
POWER
Power is also related to the concepts of energy and work. Power is defined as the rate of doing work, i.e. workdone divided by time.
Power=Workdone/Time taken
The unit of power is Watt(w)
Example 1
What is the power of a child that has done work of 60 J in 20 seconds.
Solution
Power P=Work/Time
=60/2=3 watts
Example 2
Calculate the power of a pump which can lift 500kg of water through a vertical height of 12m in 0.3 minutes. Assuming g=9.8m/s2
Force=mass x acceleration(g)
Force=500kg x9.8N
Distance=12m
Workdone =500 x9.8 x12m
Time taken= 0.3minutes x60
=18 secs
Workdone=mass x acceleration x distance
Workdone=Force x distance
Since force= mass x acceleration
Workdone=500kg x 9.8N x12m
=58800J
Power = work done/Time taken
=58800/18
Power = 3266.67 watts
Convert this to kilowatts by dividing by 1000
=3266.67/1000
=3.27kilowatts
EVALUATION
1.If the kinetic energy of a ball moving at a velocity of 5m/s is 60kj.What is the mass of the ball?
2.The mass of a ball is 10g and the height is 4m. Calculate the velocity of the ball just before it touches the ground. (g=10m/s)
3.If the mass of an object is 6kg, and the height is 5m. Calculate the potential energy. (assuming=10m/s).
4.If a force of 10Newton is applied by a car over a distance of 4metres, calculate the workdone by the car.
5.Calculate the work done by a ball of mass 40g which falls freely from a height 0.8m above the ground. (g-10m/s)
6.Calculate the power of a pump which can lift 500kg of water through a vertical height of 12m in 0.3minutes. Assuming g-9.8m/s2
See also