Question

1.
The work done by the force for x = 1 m to x = 4 m
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Answer 1

Question :

The work done by the force for x = 1m to x = 3m for the following force - position graph...

Solution :

❖ Work done is defined as the product of force and displacement.

• It is a scalar quantity having only magnitude.
• SI unit : J

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\vector(1,0){7}}\put(0,0){\vector(0,1){4}}\qbezier(0,0)(0,0)(1.5,2.5)\put(1.5,2.5){\line(1,0){1.5}}\put(1.5,-0.5){\bf1}\put(3,-0.5){\bf2}\put(4.5,-0.5){\bf3}\put(6,-0.45){\bf4}\qbezier(3,2.5)(6,0)(6,0)\multiput(3,2.5)(0,-0.3){9}{\line(0,-1){0.2}}\multiput(1.5,2.5)(0,-0.3){9}{\line(0,-1){0.2}}\multiput(1.5,2.5)(-0.3,0){5}{\line(-1,0){0.2}}\put(-0.5,2.4){\bf5}\put(7.3,0){\bf x(m)}\put(-0.15,4.3){\bf F(N)}\put(-0.4,-0.4){\bf0}\put(1.95,1){ \bf\large W_1 }\put(3.5,1){ \bf\large W_2 }\end{picture}$

★ Work = Area under the force - displacement curve between the initial and final positions of the body.

A] Work done for x = 1m to x = 2m :

➙ W₁ = Length × Breadth

➙ W₁ = (2 - 1) × (5 - 0)

➙ W₁ = 1 × 5

➙ W₁ = 5 J

B] Work done for x = 2m to x = 4m :

➙ W₂ = 1/2 × Base × Perpendicular

➙ W₂ = 1/2 × (4 - 2) × (5 - 0)

➙ W₂ = 1/2 × 2 × 5

➙ W₂ = 5 J

Net work done (W) = W₁ + W₂

➠ W = 5 + 5

➠ W = 10 J

Answer 2

Question :

The work done by the force for x = 1m to x = 3m for the following force - position graph...

Solution :

❖ Work done is defined as the product of force and displacement.

It is a scalar quantity having only magnitude.

SI unit : J

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\vector(1,0){7}}\put(0,0){\vector(0,1){4}}\qbezier(0,0)(0,0)(1.5,2.5)\put(1.5,2.5){\line(1,0){1.5}}\put(1.5,-0.5){\bf1}\put(3,-0.5){\bf2}\put(4.5,-0.5){\bf3}\put(6,-0.45){\bf4}\qbezier(3,2.5)(6,0)(6,0)\multiput(3,2.5)(0,-0.3){9}{\line(0,-1){0.2}}\multiput(1.5,2.5)(0,-0.3){9}{\line(0,-1){0.2}}\multiput(1.5,2.5)(-0.3,0){5}{\line(-1,0){0.2}}\put(-0.5,2.4){\bf5}\put(7.3,0){\bf x(m)}\put(-0.15,4.3){\bf F(N)}\put(-0.4,-0.4){\bf0}\put(1.95,1){ \bf\large W_1 }\put(3.5,1){ \bf\large W_2 }\end{picture}$

★ Work = Area under the force - displacement curve between the initial and final positions of the body.

A] Work done for x = 1m to x = 2m :

➙ W₁ = Length × Breadth

➙ W₁ = (2 - 1) × (5 - 0)

➙ W₁ = 1 × 5

➙ W₁ = 5 J

B] Work done for x = 2m to x = 4m :

➙ W₂ = 1/2 × Base × Perpendicular

➙ W₂ = 1/2 × (4 - 2) × (5 - 0)

➙ W₂ = 1/2 × 2 × 5

➙ W₂ = 5 J

Net work done (W) = W₁ + W₂

➠ W = 5 + 5

➠ W = 10 J