A 20.0 kg block is connected to a 30.0 kg block by a string that passes over a l

Question

A 20.0 kg block is connected to a 30.0 kg block by a 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 240 N/m, as shown in Figure P8.59. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0 kg block is pulled 20.0 cm down the incline (so that the 30.0 kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0 kg block is 20.0 cm above the floor (that is, when the spring is unstretched).
m/s

Explanation / Answer

Here ,

let the speed of each block is v m/s

Now , we will use conservation of energy ,

0.5 * m * v^2 + 0.5 * M * v^2 = M * g * h - M * g * h * sin(40) + 0.5 kx^2

>>

0.5 * 20 * v^2 + 0.5 * 30 * v^2 + 20 * 9.8 * 0.20 * sin(20) = 30 * 9.8 * 0.20 + 0.5 * 240 * 0.2^2

solving for v

v = 1.42 m/s

the speed of blocks is 1.42 m/s

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