Question

. A force of 10N displaces a body by a distance of 2m at an angle of 60⁰ to its own direction. Find the amount of work done.​

Answer 1

Required answer:–

Given:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{ \: ★ \: Force \: (F) = \: 10N }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{★ \: Displacement \: (S) \: = \: 2m }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{★ \: Theta \: = \: 60⁰}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

To find:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{★ \: Amount \: of \: work \: done}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

As we know,

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{★ \: Work \: done \: (W) \: = \: Force \: × \: displacement \: in}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{direction \: of \: force}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{That \: is,}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{W \: = \: F \: × \: S \: cos \: theta }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{★ \: cos \: 60⁰ \: = \: \dfrac{1}{2} }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

Step by step explaination:

Understanding the concept...

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:

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

(2) 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.

Then,

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{W \: = \: F \: × \: S \: cos \: theta }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{W \: = 10 × 2 \: cos \: 60⁰}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{W = \: 10 \: \times 2 \times\dfrac{1}{2} }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}{\begin{array}{c} \sf \blue{work \: done \: = \: 10J}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

Answer:

Amount of work done is 10 Joules or 10J

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.

Answer 2

Answer:-

$\pink{\bigstar}$ The amount of work done is $\large\leadsto\boxed{\tt\purple{10 \: J}}$

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• Given:-

Force of 10 N displaces a body by a distance of 2m at angle of 60° to its own direction.

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• To Find:-

Amount of work done = ?

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• Solution:-

We know,

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$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{W = Fs. cos \theta}}}$

where,

W = Work done

F = Force applied

S = displacement

cos θ = angle at which body is displaced

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• Substituting in the Formula:-

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➪ $\sf W = 10 \times 2 \times cos 60^{\circ}$

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➪ $\sf W = 20 \times cos 60^{\circ}$

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➪ $\sf W = 20 \times \dfrac{1}{2} \ \ \ \ \ \ \ \dashrightarrow\bf\pink{[\because cos \: 60^{\circ} = \dfrac{1}{2}]}$

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★ $\large{\bf\red{W = 10 \: J}}$

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✯ Note:- Unit of Work is Joules [J].

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Therefore, the work done is 10 J.