Question

A force of 20 N displaces a body by a distance of 2 m at an angle of 30° to its own direction. Find the amount of work done.

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

Given that: A force of 20 Newton's displaces a body by a distance of 2 metres at an angle of 30° to its own direction.

To find: The amount of work done.

Solution: The amount of work done = 20√3 Joules

Using concept: Formula to find out work done is FScosθ

• (Where, F denotes force, S denotes displacement, θ means theta and it denotes the angle)

• (Here, F is 20N , S is 2 metres, θ is 30 degree)

Knowledge required:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \tt sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \tt cos A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \tt tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \tt \infty \\ \\ \tt cosec A & \tt \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \tt sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \tt \infty \\ \\ \tt cotA & \tt \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

Full Solution:

››› Work done = FScosθ

››› Work done = 20(2)cosθ

››› Work done = 20(2)cos(30°)

››› Work done = 20(2)(√3/2)

››› Work done = 20 × 2 × √3/2

››› Work done = 40 × √3/2

››› Work done = 20 × √3

››› Work done = 20√3 J

Therefore, 20√3 J is the work done by a force of 20 N displaces a body by a distance of 2 m at an angle of 30° to its own direction.

${\large{\pmb{\sf{\underline{AdditioNal \; Knowledge...}}}}}$

Work - If a body get displaced when a force acts on it, work it said to be done. Work is measured by the product of force and displacement of the body along the direction of force. If a body get displaced by S when a force F act's on it, then the work W = FScosØ

[Where, ∅ denotes angle between force and displacement]

If both force and displacement are in the same direction, then W = FS.

• Work is a scaler quantity and it's SI unit is joules.

♛ Energy = Capacity of doing work by a body is called it's energy. Energy is a scaler quantity & it's SI unit is joule Energy developed in a body due to work done on it is called mechanical energy.

Mechanical energy is of two types –

• Potential energy
• Kinetic energy

➜ Potential energy = The capacity of doing work developed in a body due to it's position or configuration is known as potential energy like, ⑴ energy of stretched or compressed string ⑵ energy of spring in a watch ⑶ energy of water collected at a height.

• PE of a body is the gravitational field of earth is mgh

[Where, m denotes mass , g denotes acceleration due to gravity and h denotes height of the body from the surface of the earth].

➜ Kinetic energy = Energy posses by a body due to it's motion is called kinetic energy of the body. If a body of mass is moving with speed then kinetic energy of body is

• 1/2mv²

[Where, m denotes mass and v denotes speed].

Relation between kinetic energy and momentum:

• KE = p²/2m

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