work done in physics
Outside physics, work has difference meaning, include even mental activities like reading, working in offices and many more. But in physics, work means only one thing.
Work is said to be done when a force moves a body to a certain distance in direction of force. Work done is equal to the product of force and the distance moved. For example , a work is done when you drag your bag a certain distance or when a body is raised through a certain distance. In each of the example the amount of work done is equal to the product of force and the distance moved in the direction of force.
Thus work done: W = force x distance in the direction of force
Ie W =f x s, where W = work done, F = force, S = distance.
But if the force moving the body is inclined to an angle as show below,
work done = w = f x ScosѲ
The unit of measurement of work done in physics is joule J
Example if a body is pulled along a horizontal plane by a constant force of 10N applied parallel to the plane. (a) calculate the work done in moving the body 40m. (b) Calculate the work done, if the same force is used on the body for the same distance but applied at 600 the horizontal.s
Solution, (a) recall that work done = F x S, where F = force = 10n, S = distance = 40
W = F x S = 10 x 40 = 400J
(b) to solve this you first resolve the force to the horizontal
CosѲ = x/f, => x = fcosѲ,
that means that the force on the horizontal axis is equal fcosѲ
So work done in question (b) is
W = S*fcosѲ = 40 x 10 x cos60 =200J
Work done in force field
The example of force field is earth’s gravitational force field , that is the force that pulls a body toward the center of earth, To lift a body to height h, a pulling force must be applied to overcome the weight of the body. Therefore when a object is lifted up work is done against the force of gravity. The magnitude of the work done is given by, W= Mgh, where W = work done, g = force of gravity, and h = height m
Example. a man of mass 80kg carries a load of bricks of mass 20kg up a vertical ladder of length 6m. What work has he done? Solution:
W = mgh, where m = 80kg + 20kg, g = 10m-2, h = 6m. w = 100 x 10 x 6 x = 6000J =6kJ.
work done when a body falls under gravitational force.
If a body of mass m falls from a vertical height , the total work done will also be equal to mgh.
Example , if a stone of 30kg falls from a height of 5m. calculate the work done.
Solution, work done = mgh
, where m = 30kg, g = 10ms-2 and h = 5m
W = 30 x 10 x 5 = 1500J= 1.5kg.
Take note of this, from the diagram below , if a load of mass m slide down a smooth plane with inclination Ѳ, from A to B . if the same mass is dropped from A to C, a vertical distance h. in which of the two case is more work done.
Considering the work done through Ac and BA. Work done from A to C =mgh
Work done from A to B = mg x ABsinѲ, but mgh = mg x ABsinѲ
So the same work is done, this because gravitational force depends only on vertical distance moved and not the path taken.
you may like to read: Fundamental and Derived quantities,units and dimensions