Question

A force of 4 n acts on a body of mass 40 kg initially at rest for a distance of 2m. The k.E. Acquired by the body is

Answer 1

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From the Question,

• Force acting on the Body,F = 4 N

• Mass of the Body,m = 40 Kg

• Distance Covered,s = 2 m

To find

Kinetic Energy

Since,

The object is at rest,it's initial velocity is zero » u = 0 m/s

Work Done by the Force on body

$\huge{ \boxed{ \boxed{ \sf{ \green{W = fs}}}}}$

Putting the values,

$\large{ \leadsto \: \sf{W = (4)(2)}} \\ \\ \huge{ \leadsto \: \underline{ \boxed{ \rm{W = 8 \: J}}}}$

Also,

$\huge{ \boxed{ \boxed{ \sf{</p><p>f = ma}}}} \\ \\ \large{ \implies \: \sf{a = \frac{f}{m} }} \\ \\ \large{ \implies \: \sf{a = \frac{4}{40} }} \\ \\ \large{ \implies \: \boxed{ \boxed{ \sf{a = \frac{1}{10} \: m {s}^{ - 2} }}}}$

Work Energy Theorem

The work done by all the forces acting on the body is equal to change in kinetic energy of the body

$\huge{ \boxed{ \boxed{ \tt{ \green{W = {K}_{f} - {K}_{i} }}}}}$

Kinetic Energy is the half product of mass of the object and square of the velocity of the object.Initial Kinetic Energy would be zero,given : initial velocity is zero.

$\large{ \longrightarrow \: \sf{W = {K}_{f} - 0 }} \\ \\ \huge{ \longrightarrow \: \boxed{ \boxed{\sf{ {K}_{f} = 8 \: J}}}}$

Hence,the Kinetic Energy of the body is 8 J

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Answer 2

Answer:

• Kinetic Energy (K.E) = 8 Joules.

Given:

1. Force Acting (F) = 4 N.
2. Mass of the Body (M) = 40 Kg.
3. Distance Travelled = 2 meters.

Explanation:

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From Newtons Second Law of Motion.

$\large{\boxed{\bold{F = Ma}}}$

Substituting The Values.

$\large{\tt \hookrightarrow 4 = 40 \times a}$

$\large{\tt \hookrightarrow a = \dfrac{4}{40}}$

$\large{\tt \hookrightarrow a = \dfrac{\cancel{4}}{\cancel{40}}}$

$\large{\hookrightarrow{\underline{\underline{\tt a = \dfrac{1}{10}}}}}$

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Applying Kinematic equation.

$\large{\boxed{\bold{v^2 - u^2 = 2as}}}$

Substituting the values.

$\large{\tt \hookrightarrow v^2 - (0)^2 = 2 \times \dfrac{1}{10} \times 2}$

• Initial Velocity (u) = 0 m/s.
• Distance = 2 m.
• Acceleration = 1/10 m/sec².

Simplifying.

$\large{\tt \hookrightarrow v^2 - 0 = 4 \times \dfrac{1}{10}}$

$\large{\tt \hookrightarrow v^2 = \dfrac{4}{10}}$

$\large{\boxed{\tt v^2 = \dfrac{4}{10}}}$

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From Kinetic Energy.

$\large{\boxed{\bold{K.E = \dfrac{1}{2}Mv^2}}}$

Substituting the values.

$\large{\tt \hookrightarrow K.E = \dfrac{1}{2} \times 40 \times\dfrac{4}{10}}$

$\large{\tt \hookrightarrow K.E = \dfrac{1}{2} \times \cancel{40} \times\dfrac{4}{\cancel{10}}}$

$\large{\tt \hookrightarrow K.E = \dfrac{1}{2} \times 4 \times 4}$

$\large{\tt \hookrightarrow K.E = \dfrac{1}{\cancel{2}} \times \cancel{4} \times 4}$

$\large{\tt \hookrightarrow K.E = 1 \times 2 \times 4}$

$\large{\tt \hookrightarrow K.E = 1 \times 8}$

$\huge{\boxed{\boxed{\tt K.E = 8 \; J}}}$

∴ Kinetic Energy is 8 Joules.

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