How Much Energy Is Lost to Friction When a Mass Pulls Down a Spool of Wire?

[Sumbhajee]

Homework Statement

A spool of thin wire (with inner radius r = 0.45 m, outer radius R = 0.60 m, and moment of inertia Icm = 0.91 kg*m2 pivots on a shaft. The wire is pulled down by a mass M = 1.35 kg. After falling a distance D = 0.52 m, starting from rest, the mass has a speed of v = 79.900 cm/s. Calculate the energy lost to friction during that time. http://schubert.tmcc.edu/res/msu/physicslib/msuphysicslib/20_Rot2_E_Trq_Accel/graphics/prob22_pulleyD.gif

Homework Equations

The Attempt at a Solution

I have been having a lot of trouble with these rotation problems and I am not sure where to start on this. Any assistance would be appreciated.

 

[Delphi51]

Consider the types of energy involved. You start with the gravitational PE of the mass, and as it falls you lose that and get KE plus the rotational energy of the spinning spool. Write out a law of conservation of energy for those.

 

[tomcue]

I would suggest approaching this problem by first identifying the key variables and equations involved. In this case, the key variables are the moment of inertia, the mass, the distance fallen, and the final velocity. The key equations to use would be the equations for rotational kinetic energy and the work-energy theorem.

To start, we can calculate the initial rotational kinetic energy of the spool using the moment of inertia and the initial angular velocity (which can be assumed to be zero since the spool starts at rest). Then, using the work-energy theorem, we can calculate the work done by the force of gravity on the spool as it falls a distance D. This work will be equal to the change in rotational kinetic energy. Finally, we can use the equation for rotational kinetic energy again to calculate the final rotational kinetic energy, which will be equal to the initial kinetic energy minus the work done by gravity.

The difference between the initial and final rotational kinetic energies will give us the amount of energy lost due to friction. This can then be converted to the appropriate units (such as Joules) to express the energy lost in a more understandable way.

It's important to note that this approach assumes that all of the energy lost is due to friction. If there are other forces at play (such as air resistance), the calculation may be more complex and may require additional information.