Question

A 4.00 kg block hangs by a light string that passes over a massless, frictionless pulley and is connected to a 6.00 kg block that rests on a frictionless shelf. The 6.00 kg block is pushed agaisnt a spring to which it is not attached. THe spring has a spring constant of 180 N/m , and it is compressed by 30.0cm. Find the speed of the block after the spring is released and the 4.00 kg block has fallen a distance of 40.0 cm.

Answer 1

We can use the conservation of energy to solve the above problem

E stored in the spring E=1/2 kx^2 = 8.1 Joules

Work done by the friction through a slide of 0.4 m is Wf=uN = 0.2 * 6 *g = 11.76 Joules

Decrease in potential energy 4 kg = 4g*0.4 = 15.68 joules

let the speed of the blocks be v

v^2/2 * (4+6) = 12.02

which is the kinetic energy on the left are provided by energy stored in the spring and the decrease in potential energy of 4 kg minus work done against friction

v=1.55 m/sec