The System below is released from rest with the spring neither compressed nor st

Question

The System below is released from rest with the spring neither compressed nor stretched. The of spring of constant k =75 N/m is fixed, while the right end is attached to a block of mass m_1 = 19.4 kg. That block is connected by a massless cord, passing over a massless. frictionless pulley. to a block of mass m_2 = 13.7 kg which hangs freely. There is kinetic friction of coefficient fik mu_k = 0.28 between the block of mass m_1 and the surface on which it rests. Please find the v of system at the instant when the mass m_2 has fallen a distance, h = 2.7m.

Explanation / Answer

Let the final velocity, be v
Using Energy Conservation,
Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy
0 + m2*g*h = 1/2*m1*v^2 + 1/2 * m2*v^2 + 1/2*k*h^2 + uk*m1*g*h
Substituing Values,
13.7* 9.8 * 2.7 = 1/2 * (13.7+19.4) * v^2 + 1/2*75*2.7^2 + 0.28*19.4*9.8*2.7
Solving for v
16.55v^2 = - 54.5
We get to know no real solution is possible so which means that the block will not fall this distance !!

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