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Two bodies of masses m(1)and m(2) are co...

Two bodies of masses `m_(1)and m_(2)` are connected by a non-deformed light speing and lie on a horizontal plane. Coefficient of friction between the surface and the blocks is `mu.` Find an expression for the work done by the various foeces. Force F is applied horzontally to body of mass `m_(1)` in order to shift body of mass `m_(2).`

Text Solution

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Hint : `F.x=mum_(1)gx-(1)/(2)kx^(2)=0" …(i)"`
But `Kx=mum_(2)g`. (for just moving body oif mass `m_(2)`)
Put the value of K in (i) to get F
`F.x. -mum_(1)gx-(1)/(2)kx^(2)=0`
But `kx=mum_(2)g` (for moving body of mass `m_(2)`)
`Fx-mu m_(1)gx-(1)/(2)((mum_(2)g)/(x))x^(2)=0`
`F=mum_(1)g+(1)/(2)mu m_(2)g`
`=mu(m_(1)+(m_(2))/(2))g`
`=0.5(10+(10)/(2))10=75N`
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