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Mechanics

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4 Aug 2008 13:36:49 IST

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question of work energy power

None

a particle is displaced from a(0,0) to b(1,1) by a force =xy i cap along two paths 1.y=x and 2.y=x^2

a.find the work done along each paath

b.hence conclude if the force is consevative or not

plzzzz solve rates assured

thanx

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Comments (5)

debmalya choudhuri

Blazing goIITian

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4 Aug 2008 13:49:37 IST

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plzzzz answer rates assured

debmalya choudhuri

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5 Aug 2008 12:57:40 IST

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why havent any one answered the question

Sahil Pattnayak

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5 Aug 2008 13:09:24 IST

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for y=x its 1...

4 y=x2 it is also 1 till pt. 1,1

Nikhil Bhattacharya

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5 Aug 2008 13:28:59 IST

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Mukul Mathur

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5 Aug 2008 16:23:32 IST

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This is a case of variable force and variable displacement. The work done will be

W=Int₀¹ F_xdx+Int₀¹ F_ydy

since F=xy i therfore F_x=xy and F_y=0

for path y=x

F_x=x²

W=Int₀¹ F_xdx=Int₀¹ x²dx=(x³/3)₀¹=1/3

For second case y=x²

F_x=x³

W=Int₀¹ F_xdx=Int₀¹ x³dx=(x⁴/4)₀¹=1/4

Force is non conservative

Also if you see the force displacement diagram for case y=x you will notice that the area under diagram is less than that of a triangle with sides 1.

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