Solved Examples on Work Done

Example 1: The rope pulls the box along the floor, creating a 30° angle with the horizontal surface. The box is dragged for 20 meters, with a force of 90 N applied by the rope. Where can I find the force’s final work?

Solution:

Here,

The angle between force and displacement, θ = 30°

The displacement of the box, d = 20 m

The force applied on the box, F = 90 N

So, total work done by the force is,

W = F d cosθ = 90 × 20 × 0.866 J

    = 1558.8 J ≈ 1560 J

Hence, the work done by the force is 1560 J.

Example 2: With Force 10 N engaged at an angle of 60° from the horizontal, a girl thrusts a toy car from the stationary state on the horizontal floor. The toy car weighs 4 kg. In 10 seconds, can you find the girl’s work?

Solution:

Initially, we can resolve the force into two components such as horizontal and vertical component;

Horizontal component = 10 cos60° = 5 N

Vertical component = 10 sin60° = 8.66 N

Now we need to figure out how much work we’ve done and how far we’ve travelled.

Horizontal force will now be the sole source of acceleration for that toy cart.

Acceleration, a = F/m = 5 N /4 kg = 1.25 m/s²

We can obtain displacement from the formula:

s = u t + 1/2 a t² = 0 + 0.5 × 1.25 × 10² m = 62.5 m

So, the work done will be:

W = F × s 
    = 5 × 62.5 J
    = 312.5 J

Hence, the work done by the car is 312.5 J

Example 3: Calculate the Work Done on the Body when a force pg 50 N displaces it by 5m

Solution: 

Formula for the work done is,

W = F × d

Given,

F = 50 N
d = 5m

Substituting these values in the above formula we get

W = 50 × 5

W = 250 Joule

Thus, the work done on the body is 250 J.

Example 4: A Box is pulled over an inclined plane with a force of 5 KN. If the displacement of the box is 5 m and the inclination of the plane is 30°. Find the work done (neglecting the weight of the box and friction between the plane and the box)

Solution:

Force applied on the box is 5 KN = 5000 N.

As the box is placed on an inclined plane with an angle of 30° the two components of the forces are, F cos 30° and F sin 30°.

The force which displace the body is F cos 30°= 5000 × (√3 / 2)

                                                                          = 2500√3

Displacement of the box is 5 m.

Work done is given by the formula,

W = F × d

    = 2500√3 × 5 

    = 12500√3 Joule

Thus, the work done is 12500√3 J

Work is said to be done when a force (push or pull) applied to an object causes a displacement of the object. In our daily life, we do work and get tired. Even if we are doing our work while sitting on a chair, we say we have done a lot of work and got tired. But this is not the work done as per the definitions of physics.

In this article, we will learn the definition of work in terms of physics and the factors on which work depends.