Question

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in (Figure 1) . The pulley is a uniform disk with mass 10.0 kg and radius 39.0 cm and turns on frictionless bearings. You measure that the stone travels a distance 12.8 m during a time interval of 4.00 s starting from rest.

A) Find the mass of the stone.
B) Find the tension in the wire.

Answer 1

The mass of the stone can be determined by using Newton's second law and accounting for the pulley's mass and radius. Tension in the wire can also be found using the moment of inertia and angular acceleration related to rotational motion.

Step-by-step explanation:

To find the mass of the stone in a physics problem involving a pulley system, we would need to apply the principles of Newton's laws of motion and the work-energy theorem. The distance traveled by the stone, along with the time taken from rest to the final point, can provide insights into the acceleration and, in turn, the force involved in moving the stone. This force, when equated to the product of mass and acceleration (F=ma), can give us the required mass of the stone as long as the tension in the wire and the mass of the pulley system are accounted for.

The tension in the wire, which is part of a pulley system, can be found by using Newton's second law, which, in the context of rotational motion, involves the moment of inertia and angular acceleration. The tension provides the necessary centripetal force to keep the stone moving in its circular path and is a crucial factor in maintaining the system's equilibrium.