Work Energy and Power

 Work; This is the product of force and the displacement in the direction of the force.

Work done = force x distance moved in the direction of force

The unit of work done is Joule (J)

How to Calculate Work Done

Example Questions

1.        If a car of mass 80kg moved a distance of 5m. calculate the work done by the car

(g =10m/s²)

 

Solution

Mass = 80kg

Force = 80 x 10 = 800N

Distance = 5m

Work done = 800 x 5 = 4000J

2.       A boy pulls a load of 300N to a distance of 6m. Calculate the work done

 

Solution

Force = 300N

Distance = 6m

Work done = 300 X 6 = 1800J

Energy: This is the ability to do work. It is also measured in Joule (J). Energy has many forms which include:

·         Heat energy

·         Light energy

·         Chemical energy

·         Electrical energy

·         Atomic energy

·         Solar energy

·         Mechanical energy

We are going to be studying mechanical energy. Mechanical energy is divided into two

i.                     Potential energy

ii.                   Kinetic energy

Potential energy: This is stored energy or energy due to the position of an object or due to height.

P.E = mgh

M = mass

G = acceleration due to gravity

H = height of the object

How to calculate the potential energy

Example Questions

1.       Calculate the potential energy of a body of mass 8kg held 5m above the floor (g =10m/s²)

               Solution

P.E = mgh

M = 8kg

G = 10m/s²

H = 5m

P.E = 8 X 10 X 5 = 400J

2.       A loaded sack bag of mass 50kg falls down from the floor of a lorry 4m high. Calculate the work done by gravity on the load. (g = 10m/s²)

Solution

P.E = mgh

       = 50 X 10 X 4 = 2000J

Kinetic energy: This is the energy possessed by a body due to motion

K.E = ½ mv²

Where m = mass

             V = velocity

Example Questions

1.       A mass of 60kg has a velocity of 40m/s. what is its kinetic energy?

 

Solution

K.E = ½ mv²

      = ½ x 60 x 40 x 40 = 48000J

2.       A body has a mass of 20kg. if its kinetic energy is 2000J, calculate its velocity.

 

Solution

K.E = ½ mv²

2000 = ½ x 20 x V²

2000 x 2 = 20 x V²

V²   = 4000/20 = 200

V   = √200   = 14.1m/s

Power: This is the rate of doing work or work done per second.

Power = work done/ time taken

Its unit is J/s of watt (W).

Example Questions

1.       If a water pump can lift 2000kg of water through a vertical height of 20m in 20s. calculate the power of the pump. (g = 10m/s²)

 

Solution

 

Power = work done/ time taken

Force = 2000 x 10 = 20000N

Distance = 20m

Work done = 20000 x20  = 400000J

Power = 400000/20  = 20000w or 20kw

2.       A man whose mass is 80kg walks up a flight of 14 steps each 40cm high in 10s. find the power he develops in watts (g = 10m/s²)

 

Solution

 Power = mgh/time

Distance 14 x 40 = 560cm = 560/100 = 5.6m

Power = 80 x 10 x 5.6/10   = 448W