Net torque for a frictionless pulley

In summary, the net torque about the pulley axis is determined by the weight of the banana and monkey, as well as their respective distances from the pulley axis. The angular momentum of the monkey, banana, and pulley must all be taken into account in determining the motion of the system. The conservation of angular momentum means that if the initial angular momentum is not enough, the monkey will not be able to reach the bananas, but if it is enough, the monkey will be able to reach the bananas.
  • #1
Slimsta
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0

Homework Statement


A light rope passes over a light frictionless pulley. One end is fastened to a bunch of bananas of mass m, and a monkey of mass m clings to the other end of the rope. The monkey climbs the rope in an attempt to reach the bananas.
(a) Treating the system as consisting of the monkey, bananas, rope, and pulley, evaluate the net torque about the pulley axis.
(b) Using the results to (a), determine the total angular momentum about the pulley axis and describe the motion of the system. Will the monkey reach the bananas?
http://img190.imageshack.us/img190/1090/88950080.jpg [Broken]

Homework Equations


torque = FR
I=RP

The Attempt at a Solution


a. (Wbanana - Wmonkey)R
would that be right?

b.
The angular momentum of Mmonkey is Mm*r2*v/r
and Mbanana is Mb*r2*v/r

and the pulley I*v/r

adding up
(Mm+Mb)*v*r+I*v/rare my answers correct?
 
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  • #2

I would like to provide some further clarification and guidance on your solution to this problem.

Firstly, in part (a), it is important to note that the net torque about the pulley axis is not just determined by the weight of the banana and monkey, but also by their respective distances from the pulley axis. This can be represented as (Wbanana * Lbanana) - (Wmonkey * Lmonkey), where Lbanana and Lmonkey are the respective distances from the pulley axis.

In part (b), your approach is correct in terms of calculating the angular momentum of the monkey and banana, but it is important to also consider the angular momentum of the pulley itself. This can be calculated as I * ω, where I is the moment of inertia of the pulley and ω is its angular velocity.

In terms of the motion of the system, the angular momentum is conserved, meaning that it will remain constant throughout the motion. This means that if the initial angular momentum is not enough for the monkey to reach the bananas, it will not be able to reach them. However, if the initial angular momentum is enough, the monkey will be able to reach the bananas.

I hope this helps to clear up any confusion and provides a more comprehensive solution to the problem.
 

1. What is net torque for a frictionless pulley?

Net torque for a frictionless pulley is the total amount of rotational force applied to the pulley in a given system. It takes into account the forces acting on the pulley, as well as the distance between those forces and the pivot point.

2. How is net torque calculated for a frictionless pulley?

Net torque is calculated by multiplying the force applied to the pulley by the distance from the pivot point to the point where the force is applied. This is known as the lever arm. The net torque is then the sum of all the individual torques acting on the pulley.

3. Why is friction not a factor in net torque for a frictionless pulley?

In a frictionless system, there is no resistance to the motion of the pulley, so there is no force opposing the rotation. This means that there is no frictional force acting on the pulley, and therefore it does not need to be taken into account when calculating net torque.

4. What is the significance of net torque for a frictionless pulley?

Net torque is an important concept in understanding the motion and stability of a system involving a frictionless pulley. It helps determine the direction and speed of rotation, as well as the equilibrium point of the pulley. It is also used in calculating the mechanical advantage of a pulley system.

5. How does the direction of the forces affect net torque for a frictionless pulley?

The direction of the forces acting on a frictionless pulley can greatly impact the net torque. If the forces are in opposite directions, they will cancel each other out and the net torque will be zero. However, if they are in the same direction, they will add together and increase the net torque, leading to a faster rotation of the pulley.

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