Question

Two metal disks, one with radius r=2.50cm and the other with radius r= 5.00cm cm, are welded together and mounted on a frictionless axis through their common center. A string is wrapped around the edge of the small disk, and a box of mass 1.5 kg is tied to the end of the string. The box is released from rest and descends downward while the total moment of inertia of the two disks is 22.5kg .cm². Calculate the acceleration of the hanging box after it is released.

A) 1.6m/s²
B) 2.4m/s²
C) 3.2m/s²
D) 4.8m/s²

Answer 1

To calculate the acceleration of the hanging box, find the moment of inertia of the two disks, calculate the net torque applied to the system, and use the equation Torque = Moment of Inertia * Angular Acceleration to find the angular acceleration, which is equal to the acceleration of the hanging box.

Step-by-step explanation:

To calculate the acceleration of the hanging box, we need to use the principles of rotational motion. First, we need to find the moment of inertia of the two disks. We are given that the total moment of inertia is 22.5 kg.cm². Since the moment of inertia of a disk is given by 0.5 * mass * radius², we can set up the equation as follows:

0.5 * m1 * r1² + 0.5 * m2 * r2² = 22.5 kg.cm²

Plugging in the given values for r1, r2, and the masses of the two disks, we can solve for m1 and m2. Once we have the masses, we can use the force applied to the small disk (which is equal to the weight of the hanging box) to find the net torque applied to the system using the formula:

Torque = Force * Radius

Finally, we can use the equation:

Torque = Moment of Inertia * Angular Acceleration

to find the angular acceleration, which is equal to the acceleration of the hanging box. Converting the angular acceleration from rad/s² to m/s² will give us the answer.