Pulley with Mass: Impact on Energy and Work Questions - Explained

[devanlevin]

in all energy and work questions i have had till now, the mass of pulleys have not been taken into account, if they had, would the system's kinetic energy have increased?
it seems to me that a pulley with mass would have velocity and acceleration and therefore would have its own kinetic energy,
if the system started from resting point, then the total work would be W=EK1, ie kinetic energy of the system, whereas with a pulley with mass W=EK1+EK2 ie knetic energy of the system as it was and kinetic energy of the pulley, the system as a whole will manage the same work with less EK1, is this logical?? what does it mean? will it pass the same distance but with lesser velocity?
is this point only valid if there is friction between the pulley and the rope or would this still affect the rest of the system if there was no friction whatsoever?

 

[mukundpa]

What will make the pulley rotate?
If the pulley will rotate, will it have kinetic energy?

 

[baba89]

The inclusion of the mass of the pulley in energy and work questions can have a significant impact on the overall system's kinetic energy. As you mentioned, a pulley with mass will have its own velocity and acceleration, and therefore its own kinetic energy. This means that the total kinetic energy of the system will be the sum of the kinetic energy of the system as a whole and the kinetic energy of the pulley.

In a system where the pulley is at rest, the total work done would be equal to the kinetic energy of the system (W=EK1). However, if the pulley has mass, the total work done would be the sum of the kinetic energy of the system and the pulley (W=EK1 + EK2). This means that the system as a whole would have the same amount of work, but with less kinetic energy (EK1) because some of the work is now being used to move the pulley (EK2). This can result in a decrease in the system's velocity.

This concept holds true regardless of whether there is friction between the pulley and the rope or not. The mass of the pulley will still have an impact on the overall system's kinetic energy and work, even without friction.

In conclusion, the inclusion of the mass of the pulley in energy and work questions is important to consider, as it can affect the overall dynamics of the system and the amount of work required to move it. It is essential to take into account all components of a system, including the pulley, to accurately calculate and understand the energy and work involved.