What is the acceleration of the blockandtrolley system shown in a Fig.(a), if the coefficient of kinetic friction between the trolley and the surface is 0.04? What is the tension in the string? (Take g = 10 m s^(-2) ).Neglect the mass of the string.

What is the acceleration of the blockandtrolley system shown in a Fig.

1.	What is the acceleration of the blockandtrolley system shown in a Fig.(a), if the coefficient of kinetic friction between the trolley and the surface is 0.04? What is the tension in the string? (Take g = 10 m s^(-2) ).Neglect the mass of the string.
Answer» Solution :As the string is INEXTENSIBLE and the pully is smooth, the 3 kg block and the 20 kg trolley both have same magnitude of acceleration.Applying second law to motion of the block (Fig. (b)) `30 - T = 3a` Apply the second law to motion of the trolley (Fig. (c)), `T - f_k = 20a` `f_k = mu_k N` ` mu_k = 0.04` `N = 20 xx 10` = 200N Thus the equation for the motion of the trolley is `T - 0.04 xx 200 = 20 a " or" T - 8 = 20a ` These EQUATIONS give a ` = 22/23 ms^(-2) = 0.96 ms^(-2)`and T = 27.1 N