Rotational Kinetic Energy and Work

[parwana]

The puck in Figure P8.51 has a mass of 0.120 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 85.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Hint: Consider the change of kinetic energy of the puck.)

I tried doing it by finding the Kinetic Rotational Energy before and after but its not coming out right. For the KE after do I use the radius as 15, or is it 40-15?

 

[Doc Al]

The puck ends up 15 cm closer to the center, so its new radius will be 40-15 cm.

 

[kyle8921]

I would approach this problem by first defining the concepts of rotational kinetic energy and work. Rotational kinetic energy is the energy an object possesses due to its rotation, and it is expressed as 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Work, on the other hand, is the force applied to an object multiplied by the distance over which the force is applied.

In this scenario, the puck has an initial rotational kinetic energy due to its original distance from the center of rotation and its speed. As the string is pulled downward, the puck's distance from the center of rotation decreases, causing a change in its moment of inertia. This change in moment of inertia results in a change in the puck's rotational kinetic energy.

To determine the work done on the puck, we need to consider the change in the puck's kinetic energy. The final kinetic energy of the puck will be equal to its initial kinetic energy plus the work done on it. Therefore, we need to find the final kinetic energy of the puck after the string is pulled downward.

To calculate the final kinetic energy, we need to use the new distance from the center of rotation, which is 40 cm - 15 cm = 25 cm. We also need to calculate the new angular velocity of the puck, which can be found using the conservation of angular momentum. The moment of inertia of a puck rotating about its center is given by I = mr^2, where m is the mass of the puck and r is the distance from the center of rotation. Using this formula and the given values, we can calculate the initial and final angular velocities of the puck.

Once we have the final kinetic energy of the puck, we can subtract the initial kinetic energy from it to find the work done on the puck. This work represents the change in the puck's kinetic energy due to the change in its moment of inertia.

In conclusion, the work done on the puck can be found by considering the change in its kinetic energy, which is a result of the change in its moment of inertia. It is important to use the correct values for the distance and angular velocity when calculating the final kinetic energy of the puck.