Question

A body is pulled along a horizontal plane through a distance of 5 m by applying a constant force of 4 N. Find the work done by the force when- i) the force is applied along the plane and ii) the force is applied at an angle of 600 with the plane.

Answer 1

Given :-

Force = F = 5 N

Distance = d = 5 m

As we know that work done is the dot product of force and distance/displacement. But in the first case theta is not defined we can assume theta as 0°.

i). W = F•d

W = 5 × 4 × Cos 0°

$\bf{W\:=\:20\:Joules}$

ii). In this case theta is defined as 60° therefore we will put its value in the formula used above.

W = 4 × 5 × Cos 60°

W = 20 × 1/2

$\bf{W\:=\:10\:Joules}$

It is important to note that maximum work will be done when defined theta is 0° and on any defined theta except 0° work done will be less as compared to work done on 0°.

Answer 2

Given :-

A body is pulled along a horizontal plane through a distance of 5 m by applying a constant force of 4 N

To Find :-

i) the force is applied along the plane and ii) the force is applied at an angle of 60 with the plane.

Solution :-

1]

We know that

W = fs

where

W = work done

F = force applied

s = distance

W = 4 × 5

W = 20 J

2]

When angle is given

W = fs cosΘ

Where

W = work done

F = force applied

s = distance

cosΘ = angle made

W = 4 × 5 × cos(60)

As cos 60 = 1/2

W = 4 × 5 × 1/2

W = 2 × 5 × 1

W = 10 J

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