Calculation of Work Done


 
 
Concept Explanation
 

Calculation of Work Done

Calcualtion of the Work Done: The work done by a body is the product of the force and displacement in the direction of force

                 W = F. s costheta

Where, F = Force is equal to force applied

             s = dispalcement of the body

            costheta = cosine value of the angle between force  and displacement or the direction of motion

Q. A body of mass 2 kg is raised to a height of 1m. Find the work done by the force of gravity?

Solution:  The force of gravity on the body, is the force exerted by earth on it = mg acting vertically downward.

However the displacement s = 1m vertically upwards

The angle between Force of Gravity and Direction of Motion

            theta= 180^0

   Now from W = Fs costheta  =  mgcostheta

                     W = 2 x 9.8 x 1 x cos 180^{circ}

                        =  - 19.6 J (because  cos 180^{circ} = -1)

Q. A force of 10 N displaces by 5 m, the angle between force and displacement is 60^{circ}, then find the work done. 

Solution: F = 10N, s  =  5 m

Angle between force and displacement ,  theta;=;60^{circ}

Work done, W =Fd cos theta = 10 x 5 x cos 60^{circ}

                  W;=;10times;5;timesfrac{1}{2};;;;;[where ; cos 60^0 = frac{1}{2}]

                 W = 25 J

Sample Questions
(More Questions for each concept available in Login)
Question : 1

How much work is done by a force of 10 N in moving an object through a distance of 5 m in the direction opposite to the force?

Right Option : C
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Explanation
Question : 2

If force and displacement of particle in direction of force are doubled. Work would be

Right Option : B
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Explanation
Question : 3

A car weighing 500 kg. working against a resistance of 500N, accelerates from rest to 20m/s in 100m.(g=10m/s^{2}). The work done by the engine of car is

Right Option : B
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Explanation
 
 


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