A block of mass m = 1 kg rests on top of a larger block of mass M = 4 kg. The larger block is placed on a smooth horizontal surface and is connected to a rigid wall by a horizontal spring of unknown spring constant k . The coefficient of static friction between the two blocks is = 0.5 . The system is set into simple harmonic motion. If the maximum kinetic energy of the system such that the upper block just avoids sli

Step-by-step solution

For the upper block not to slip, its maximum acceleration must not exceed the acceleration provided by limiting static friction. The maximum frictional force on the upper block is: f_ = m g = 0.5 1 10 = 5 N The maximum acceleration of the system is therefore: a_ = f_ m = 5 1 = 5 m/s ^2 The angular frequency of the two-block system is given by ^2 = k M+m = k 5 . Using the relation for maximum acceleration in SHM, a_ = ^2 A , we find the amplitude A : 5 = ( k 5 ) A A = 25 k The maximum kinetic energy of the system is