Question

calculate the work done if the force of 30 N acts on a body and it moves at a distance of 4 m and makes angle of 60 degree to horizontal surface ​

Answer 1

Answer:

• Force (F) = 30 N
• Displacement (S) = 4 m
• Angle made in b/w force and displacement (θ) = 60°
• Work done = ?

•Work done is difined as : W = FS cos(θ)

• Work is a scalar quantity.

• SI unit of work is Joule (J) or N-m.

• Dimensional formula : [W] = [ML²T-²]

$\longrightarrow\tt W = FS \cos(\theta)$

$\longrightarrow\tt W = 30 \times 4 \times \cos( {60}^{ \circ} )$

$\longrightarrow\tt W = 30 \times 4 \times \dfrac{1}{2}$

$\longrightarrow\tt W = 30 \times 2$

$\longrightarrow \underline{ \boxed{\bold{W = 60 \:J}}}$

Answer 2

❖ Given:-

• Force = 30N
• Distance travelled = 4 m

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❖ Need to find?

• Work done.

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❖ Formula to be used:-

• Work done = F × S cos θ

Or

• W = F × S cos θ

where,

• F = Force

• S cos θ = Displacement in direction of force

• Cos = 1/2

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❖ A general explaination:

A force displaces the body in a direction other than the direction of force, then we can determine the amount of work done by the two ways:

(i) by finding the component of displacement of the body in the direction of force.

(ii) By finding the component of force in the direction of displacement.

Way used in the given answer:

★ finding the component of displacement of the body in the direction of force.

❖ Answer:

First of all we will be substituting the values in the given formula. And we already knew that value of cos 60⁰ is 1/2.

$\: \: \: \: : \implies \: \text{W} = \bold{30 \times 4 \times \dfrac{1}{2} }$

Reducing to their lowest terms.

$\: \: \: \: : \implies \: \text{W} = \bold{ \cancel{30} \: \:{}^{15} \times 4 \times \dfrac{1}{ \cancel2} }$

$\: \: \: \: : \implies \: \text{W} = \bold{15 \times 4}$

$\: \: \: \: : \implies \: \text{W} = \bold{60}$

Thus,

Work done is 60 Joules or 60J

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❖ Extra information:-

Work is said to be done only when a the force applied on a body makes the body move (i.e., there is a displacement of body.

★The amount of work done depends on two factors:

• magnitude of force applied
• displacement produced by the force.

★ The amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force.

★ If a force acts on a body and the body does not move i.e., displacement is zero, then no work is done.

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