Heavy Pulley / Conservation of Mechanical Energy

In summary, the conversation is about using conservation of mechanical energy to calculate the speed of a block attached to a light inextensible string wrapped around a cylindrical pulley. The conversation discusses the need for the angular velocity ω, which can be expressed in terms of linear velocity v, and the misconception that knowledge of the pulley's radius is necessary for solving the problem. It is mentioned that the ω2 term in the equation can be cancelled out by the r2 term in the moment of inertia, allowing for the use of v alone.
  • #1
danrochester
9
0

Homework Statement


A light inextensible string is wrapped around a cylindrical pulley of mass M that is free to rotate about its axis. The end of the string is attached to a block of mass m. Use conservation of mechanical energy to calculate the speed of the block after it has fallen a distance d starting from rest.



Homework Equations


Well this is the thing, I can easily write the equation for conservation of energy, but at some point I need to know omega, the angular velocity, which I don't think I have any way of knowing.



The Attempt at a Solution


I'm not looking for the answer here, just a hint. I can think of how to do this problem if I knew the radius of the pulley; then I could easily determine omega from v = omega*r. Is there a way to distribute the change in gravitational potential energy between the linear and rotational kinetic energies of the block and pulley that doesn't require any knowledge of the radius of the pulley?
 
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  • #2
Since v = ωr, you can express the angular velocity in terms of linear velocity. You don't need to know the actual radius.
 
  • #3
danrochester said:
A light inextensible string is wrapped around a cylindrical pulley of mass M that is free to rotate about its axis.
…
I can think of how to do this problem if I knew the radius of the pulley; then I could easily determine omega from v = omega*r …

Hi danrochester! :smile:

(have an omega: ω :wink:)

You think you need the r to work out (1/2)Iω2 …

but actually you can use v on its own, because the r2 in the ω2 cancels out with the r2 in the I. :wink:
 
  • #4
no crap

haha thanks guys...Sometimes you keep digging until you're too deep to get out, and sometimes you just need to keep digging a liiiittle bit further...
 
  • #5
Homer Simpson's advice was …

No! Dig up! :biggrin:​
 

FAQ: Heavy Pulley / Conservation of Mechanical Energy

1. What is a heavy pulley?

A heavy pulley is a type of pulley that is designed to support and transfer the weight of heavy objects. It typically has a larger diameter and stronger construction compared to standard pulleys.

2. How does a heavy pulley work?

A heavy pulley works by utilizing the principle of mechanical advantage. It reduces the amount of force needed to lift a heavy object by distributing the weight over multiple ropes or cables, and redirecting the force in a more manageable direction.

3. What is the conservation of mechanical energy?

The conservation of mechanical energy is a fundamental principle in physics that states that the total amount of energy in a closed system remains constant. This means that energy cannot be created or destroyed, but can only be converted from one form to another.

4. How is conservation of mechanical energy related to heavy pulleys?

In heavy pulley systems, the conservation of mechanical energy is important because it ensures that the total amount of energy used to lift an object is equal to the total amount of energy gained by the object. This means that the work done by the force applied to the pulley system is equal to the potential energy gained by the object.

5. What are some real-world applications of heavy pulleys and conservation of mechanical energy?

Heavy pulleys and the conservation of mechanical energy are used in a variety of real-world applications, such as elevators, cranes, and weightlifting machines. They are also commonly used in industrial settings for lifting and moving heavy objects, as well as in the construction of large structures such as bridges and buildings.

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