1.9.1 Work

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Work

  1. Work done by a constant force is given by the product of the force and the distance moved in the direction of the force.
  2. The unit of Nm(Newton metre) or J(Joule).
  3. Work is a scalar quantity.
Equation of Work

When the direction of force and motion are same, θ = 0o, therefore cosθ = 1

Work done,

W = F × s


Example 1

A force of 50 N acts on the block at the angle shown in the diagram. The block moves a horizontal distance of 3.0 m. Calculate the work being done by the force.

Answer:

Work done,
W = F × s × cos θ
W = 50 × 3.0 × cos30o = 129.9J


Example 2

Diagram above shows a 10N force is pulling a metal. The friction between the block and the floor is 5N. If the distance travelled by the metal block is 2m, find

  1. the work done by the pulling force
  2. the work done by the frictional force

Asnwer:

(a) The force is in the same direction of the motion. Work done by the pulling force,

W = F × s = (10)(2) = 20J

(b) The force is not in the same direction of motion, work done by the frictional force

W = F × s × cos180o= (5)(2)(-1) = -10J


Work Done Against the Force of Gravity

Example 3
Ranjit runs up a staircase of 35 steps. Each steps is 15cm in height. Given that Ranjit's mass is 45kg, find the work done by Ranjit to reach the top of the staircase.

Answer:

In this case, Ranjit does work to overcome the gravity.
Ranjit's mass = 45kg
Vertical height of the motion, h = 35 × 0.15
Gravitational field strength, g = 10 ms-2
Work done, W = ?

W = mgh = (45)(10)(35 × 0.15) = 2362.5J


Finding Work from Force-Displacement Graph
In a Force-Displacement graph, work done is equal to the area in between the graph and the horizontal axis.

Example 4

The graph above shows the force acting on a trolley of 5 kg mass over a distance of 10 m. Find the work done by the force to move the trolley.

Answer:

In a Force-Displacement graph, work done is equal to the area below the graph. Therefore, work done

            W = \frac{1}{2} \times 8 \times 10 = 40J


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