Question

A force of 40 N acting on a body at an angle of 60 degree with the horizontal direction displaces the body through a distance of 5m along the surface of a floor. calculate the work done.​

Answer 1

Given :

• Force Applied on the body = 40 N

• Angle between direction of force and displacement = 60°

• Displacement = 5 m

To Find :

⠀⠀⠀⠀⠀⠀⠀The work done on the body.

Solution :

To find the work done , let's know about some of the cases of work done :-

• If θ < 90° , then the work done will be positive as cos θ > 0 , when 0° < θ < 90°.

• If θ > 90° , then the work done will be negative as cos θ < 0 , when 90° < θ < 180° .

• If θ = 90° , then the work done will be equal to zero as cos 90° = 0.

Here , we know the θ (i.e, 60°) is less than 90°.

Hence, the work done by the body will be positive.

We know the formula for work done .i.e,

$\underline{\boxed{\bf{W = Fs\:cos\:\theta}}}$

Where :-

• W = Work Done.

• F = Force Applied.

• s = Displacement.

• θ = Angle between direction of force and displacement.

Using the formula and substituting the values in it, we get :-

$:\implies \bf{W = Fs\:cos\:\theta}$

$:\implies \bf{W = 40 \times 5 \times cos\:60^{\circ}}$

$:\implies \bf{W = 200 \times cos\:60^{\circ}}$

$:\implies \bf{W = 200 \times \dfrac{1}{2}}\:\:\:\bigg(\because cos\:60^{\circ} = \dfrac{1}{2}\bigg)$

$:\implies \bf{W = 100}$

$\therefore \bf{Work\:Done = 100\:J}$

Hence, the work done on the body is 100 J.

Answer 2

Question:-

A force of 40 N acting on a body at an angle of 60 degree with the horizontal direction displaces the body through a distance of 5m along the surface of a floor. calculate the work done.

Formula to be used:-

⟹W=Fscosθ

Solution:-

️ ➭ W = Fscosθ

️ ➭ W = 40 × 5 × cos 60°

️ ➭ W = 200 . 1/2

️ ➭ W = 100J

☞ Hence verified