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Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop. There is no friction between block A and tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest

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We have that for the Question ,it can be said that the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest is

M=39kg

From the question we are told

  • Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop.
  • There is no friction between block A and tabletop, but the coefficient of static friction between block A and block B is 0.750.
  • A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string.
  • What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest

Generally the equation for the Static force is mathematically given as

[tex]f=umg\\\\f=0.75*5*9.8\\\f=36.75[/tex]

Generally the equation for the acceleration is mathematically given as

[tex]a=\frac{f}{m}\\\\a=\frac{36.75}{5}\\\\a=7.35m/s^2[/tex]

Therefore

[tex]F=mg\\\\9.8M=(95.55+7.35M)[/tex]

M=39kg

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