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प्रश्न
In the following figure shows a small block of mass m kept at the left end of a larger block of mass M and length l. The system can slide on a horizontal road. The system is started towards right with an initial velocity v. The friction coefficient between the road and the bigger block is μ and that between the block is μ/2. Find the time elapsed before the smaller blocks separates from the bigger block.
उत्तर
Let a1 and a2 be the accelerations of masses m and M, respectively.
Also, a1 > a2 so that mass m moves on mass M.
Let after time t, mass m is separated from mass M.
Using the equation of motion
During this time, mass m covers `ct+1/2a_1t^2` and `s_m=vt+1/2a_2t^2`.
For mass m to separate from mass M, we have: `vt+1/2a_1t^2 = vt+1/2a_2t^2+1` ........(ii)
From the free body diagram, we have:
`ma_1+mu/2"R"=0`
`=>ma_1=-(mu/2)"mg"=(mu/2)mxx10`a1 = - 5µ
Again,
`Ma_2+mu("M""m")g-(mu/2)mg=0`
⇒ 2Ma2 + 2μ (M + m)g − μmg = 0
⇒ 2Ma2 = μmg − 2μmg − 2μmg
`=> a_2=(-mumg-2muMg)/(2M)`
Substituting the values of a1 and a2 in equation (i), we get:
`t = sqrt(4Ml)/((M+m)mug)`
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