Question

14. A position dependent force F acting on a particle and its force-position curve is shown in the figure. The work done by force from x = 1 m to x = 4 m is F(N) 20 A x(m) N+ 3 18 -20+ (1) 35 J (2) -20 J (3) -15 J (4) 20 J​

Answer 1

Answer:

Solution

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Correct option is D)

Work done by a force is given by :

W=∫F.dx

So, Area under F−x (Force position) curve gives work done.

⇒ Area above x-axis is taken as positive and the area below x-axis is taken as negative.

A

1

= area above x - axis = (area of ΔOAB ) + (area of rectangle ABCD) + (area of triangle CDE)

⇒A

1

=+[

2

1

(1−0)×10+(2−1)×10+

2

1

×(3−2)×10]$

⇒A

1

=+(5+10+5)=+20 unit

A

2

= area below X-axis = (area of triangle EFH ) + (area of rectangle MFGH)

A

2

=−[

2

1

(4−3)×10+(5−4)×10]=−[5+10]=−15 unit

Net area =A

1

+A

2

=+20+(−15)=5 unit

So, work done = Net area under F−x curve =5J