Answer to Question #186730 in Classical Mechanics for R Q

Question

A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m.The spring is unstretched when the system is as shown in the figure, and the incline has a coefficient of friction of 0.2. The 20.0-kg block is pulled a distance d = 20.0 cm down the incline of angle of 30.0 degrees and released from rest. Find the speed of each block when the spring is again unstretched.

Answer 1

$U_1+K_1=U_2+K_2+W,$

$K_1=0,$

$m_2gh+\frac 12 kh^2=m_1gh\sin \alpha+\frac 12 (m_1+m_2)v^2+\mu m_1g \cos\alpha,$

$30\cdot 9.8\cdot0.2+0.5\cdot 250\cdot 0.2^2=20\cdot 9.8\cdot 0.2\cdot 0.5+0.5\cdot (20+30)\cdot v^2+0.2\cdot 20\cdot 9.8\cdot 0.87,$

$v=0.64~\frac ms.$