Question

Two blocks of mass M1 = 30 kg and M2 = 20 kg are at rest. Block M1 sits on a frictionless incline that makes an angle of 30 degrees with the horizontal. It is connected to block M2 by means of a massless rope that runs parallel to the incline and passes over a frictionless pulley. Block M2 is connected to the other end of the rope and hangs vertically. Block M2 is also connected to a massless spring mounted vertically on the floor, and sits 20 cm above the floor. The spring constant is 490 N/m.

a) Is the spring deformed?
b) Now we pull block M1 20 cm down the incline and release it from rest. When the two blocks return to their original positions, what is their speed?

Answer 1

a) The spring is deformed when block M1 is pulled down the incline. b) The speed of the blocks when they return to their original positions will depend on the amount of potential energy stored in the spring and the mass of the two blocks.

Step-by-step explanation:

a) The spring is deformed when block M1 is pulled down the incline. This is because the force of gravity on block M2 causes the rope to tighten, which in turn compresses the spring.

b) When block M1 is released, it will start moving back up the incline. As the two blocks return to their original positions, the potential energy stored in the spring will be converted into kinetic energy. Therefore, the speed of the blocks when they return to their original positions will depend on the amount of potential energy stored in the spring and the mass of the two blocks.