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A large box of mass M is pulled across a horizontal frictionless surface by a...

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sportsmaniac | Student | Honors

Posted September 30, 2012 at 1:48 AM via web

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A large box of mass M is pulled across a horizontal frictionless surface by a horizontal rope with tension T.

 

A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are mu_s (static friction) and mu_k (kinetic friction) respectively. Find an expression for the maximum tension Tmax for which the small box rides on top of the large box without slipping.

Tagged with math, mechanics, physics

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quantatanu | Student , Undergraduate | Valedictorian

Posted October 4, 2012 at 4:37 AM (Answer #3)

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I am sorry but actually I thought the coefficient of kinetic friction was beteen the bottom surface and big box, but actually its frictionless, so actually you don't need to consider mu_k, as the small box is not sliding but siting steady over the big box, so there is no use ofm_kand so every where we putm_k =0  in the above result and we will get the right answer. So let me write it down completely:

______________________________________________

Let us think that the "small" box is sitting steady over the "big" box , so the condition will be:

Acceleration of small box (a) = Acceleration of the big box  -----(1)

Now let us first calculate the acceleration of the big box:

forces on the Big Box are:

(1) Tension T along +x direction say.

(2) (M+m) * a, along +x direction too. Because rope is pulling

                      big and small box together.

 

So we set the equation:

(M+m) * a = T

=> a = T /(M+m)

 

Now we go for the small box:

Forces on the Small Box are:

(i) Force exerted by the big box on small box and that is = 

force of friction m*a along -x direction

(ii) m*a along +x direction

and these two forces are exactly equal that is why it is not moving.

So

mu_s * m * g = m * a

=> mu_s g = [T/(M+m)]

=> T = m_u * (M+m) * g

Which is the maximum tension in the rope.

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quantatanu | Student , Undergraduate | Valedictorian

Posted October 4, 2012 at 4:39 AM (Answer #2)

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wherem_u = mu_s  ofcourse.

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