Find Mass of Pulley: Solve with Torque & Impulse Calculations

[Todd88]

Homework Statement

A light string is wrapped around the outer rim of a solid uniform cylinder of diameter 75.0cm that can rotate without friction about an axle through its center. A 3.00kg stone is tied to the free end of the string. When the system is released from rest, you determine that the stone reaches a speed of 3.50m/s after having fallen 2.50m.

What is the mass of the cylinder?

Homework Equations

net torque = I * alpha
I = m * r^2 / 2

The Attempt at a Solution

For this problem I have no idea where to start. I am completely lost...I know there should be some Omega calculations a theta calculations and I need to find impulse along with torque...any help is appreciated!

 

[Doc Al]

You need to analyze both the pulley and the falling stone. Write Newton's 2nd law for each, then combine the equations to relate pulley mass to the acceleration of the stone.

Use the given data to determine the acceleration of the stone.

 

[nlightner]

I understand your confusion and desire for help with this problem. Solving for the mass of the cylinder in this scenario requires a combination of torque and impulse calculations. To start, we can use the equation for net torque, which is equal to the moment of inertia (I) multiplied by the angular acceleration (alpha). The moment of inertia for a solid cylinder rotating around its center is given by the equation I = m * r^2 / 2, where m is the mass of the cylinder and r is its radius.

Next, we need to consider the impulse, which is the change in momentum of the system. In this case, the only force acting on the system is the tension in the string, which causes the stone to accelerate downwards. Using the equation for impulse, which is equal to the force (F) multiplied by the time (t), we can solve for the force acting on the stone.

Now, we can use the equation for torque, which is equal to the force (F) multiplied by the distance (d) from the axis of rotation, to solve for the torque acting on the cylinder. This torque is equal to the net torque calculated earlier, so we can set the two equations equal to each other and solve for the mass of the cylinder.

Once we have the mass of the cylinder, we can use it to calculate the moment of inertia and solve for the angular acceleration (alpha). From there, we can use the equations for rotational kinematics to find the final angular velocity (omega) of the cylinder, and then use the equation for linear velocity (v = r * omega) to find the final speed of the stone.

I hope this helps guide you towards the solution to this problem. Remember to carefully consider all the forces and equations involved, and don't hesitate to reach out for further assistance if needed. As a scientist, it's important to approach problems with an analytical and logical mindset, and to always seek understanding and clarity. Good luck!