A 4-kg block is connected to a 10-kg block by a light string that passes over a
ID: 1913320 • Letter: A
Question
A 4-kg block is connected to a 10-kg block by a light string that passes over a frictionless pulley (solid cylinder) having a mass of 0.5 kg and a radius of 2 cm. The 10-kg block is connected to a spring of negligible mass with force constant 250 N/m, as shown. The spring is unstretched when the system is as shown in the figure. The incline is rough with a coefficient of kinetic friction equal to 0.2. The 4-kg block is pulled a distance of 10 cm down the incline (so that the 10-kg block is then 40 cm above the floor) and is released from rest. Find the speed of each block when the 10-kg block is once again at a height of 30 cm above the floor (that is when the spring is once again unstretched). Note that the 10-kg block remains connected to the spring during the motions.
Explanation / Answer
conservation of energy. energy of m1 + energy of m2 + energy stored in spring. initial energy = 10 X 0.1 X 9.8 - 4 X 0.1 X 9.8 X sin 40 + 1/2 X 250 X 0.1 ^2 final energy = 1/2 m1 v1^2 + 1/2 m2 v2^2 since the string is taut all the time, v1 = v2 work done by friction = - 0.2 X 4 X 9.8 X cos 40 X 0.1 X sin 40 ( negative wok by friction) initial energy = final energy + work done.