How Does Pulley Torque Affect Wire Tension in a Frictionless System?

In summary, a 12.0kg box and a 5.00kg weight are connected by a thin, light wire passing over a frictionless pulley. The pulley has a mass of 1.70kg and a diameter of 0.600m. After the system is released, the horizontal tension in the wire can be found by considering the net torque on the pulley and relating the angular acceleration of the pulley to the acceleration of the wire. The inextensible wire ensures that all the accelerations in the system are the same.
  • #1
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Homework Statement



A 12.0kg box resting on a horizontal, frictionless surface is attached to a 5.00kgweight by a thin, light wire that passes without slippage over a frictionless pulley (the figure ). The pulley has the shape of a uniform solid disk of mass 1.70kg and diameter 0.600 m.
After the system is released, find the horizontal tension in the wire.

http://session.masteringphysics.com/problemAsset/1037926/6/YF-10-44.jpg

Homework Equations





The Attempt at a Solution


I'm thinking of approaching it as I would if the pulley was massless by setting m1a= Thorz and m2a=m2g-Tvert, but I don't know where the pulley would come in
 
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  • #2
There will be different tensions on either side of the pulley. The net torque on the pulley will be due to the actions of the two tensions. The angular acceleration of the pulley will be dictated by the net torque and its moment of inertia. The horizontal tension determines the acceleration of M1. The vertical tension, in concert with force due to gravity on M2, determines the acceleration of M2. The inextensible wire endures that all the accelerations are the same.

Relate the angular acceleration of the pulley to the acceleration of the wire in order to tie everything together.
 

1. What is a pulley torque problem?

A pulley torque problem is a type of physics problem that involves calculating the rotational force, or torque, on a pulley system. This is typically done by considering the forces acting on the pulley and using equations to determine the net torque.

2. How do you solve a pulley torque problem?

To solve a pulley torque problem, you first need to identify all the forces acting on the pulley, including the weight of the object(s) being lifted and any tension in the ropes or cables. Then, you can use the equation τ = r x F to calculate the torque, where τ is the torque, r is the radius of the pulley, and F is the force. Finally, you can use the principle of torque equilibrium to determine the unknown variables.

3. What are the key principles involved in solving a pulley torque problem?

The key principles involved in solving a pulley torque problem are Newton's laws of motion, the principle of torque equilibrium, and the concept of mechanical advantage. Newton's laws describe the relationship between forces, masses, and acceleration, while the principle of torque equilibrium states that the sum of the torques acting on a stationary object must be zero. The mechanical advantage of a pulley system is the ratio of the output force to the input force.

4. How can I check my answer for a pulley torque problem?

To check your answer for a pulley torque problem, you can use the equation τ = r x F to calculate the torque on both sides of the pulley system. If the torques are equal, then your answer is likely correct. You can also double-check your calculations and make sure you have considered all the forces acting on the pulley.

5. Why are pulley torque problems important?

Pulley torque problems are important because they help us understand the principles of mechanics and how forces can be used to lift heavy objects. They also have practical applications, such as in engineering and construction, where pulley systems are often used to lift and move heavy loads. By solving pulley torque problems, we can also gain a better understanding of how machines work and how to calculate their efficiency.

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