What are the forces and torques acting on the masses and pulley in this system?

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Then, use the equations for torque and force to solve for the acceleration and tensions in the system.
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Homework Statement


A mass [tex]m_{1}[/tex] is hanging from a light cord which is strung over a pulley of moment of inertia, I, and radius [tex]R_{0}[/tex] and connected to a mass [tex]m_{2}[/tex] which is sliding on a rough horizontal surface with coefficient of friction [tex]\mu_{k}[/tex].

a) What is the acceleration of the system?
b) What are the tensions in each part of the cord?

All help is appreciated! :)

pulley.jpg




Homework Equations


[tex]\Sigma[/tex]F = ma
[tex]\Sigma\tau[/tex] = m[tex]R^{2}\alpha[/tex]

The Attempt at a Solution


I started by trying to sum up all the forces and torques but I don't know where to go from there.

[tex]\Sigma F_{x} = T - \mu m_{1}g = (\mu m_{1} + m_{2})g = ma[/tex]
[tex]\Sigma F_{y} = T = m_{2}g[/tex]
[tex]\Sigma \tau = rF_{x} + rF_{y}[/tex]
 
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  • #2
Always start by drawing a free-body diagram on each object, including the pulley, and writing out Newton's second law for each object.
 

1. What is a pulley?

A pulley is a simple machine that is used to lift or move heavy objects. It consists of a wheel with a grooved rim and a rope or cable that runs along the groove.

2. How does a pulley work?

A pulley works by changing the direction of the force needed to lift an object. By using a pulley, the force needed to lift the object is spread out over multiple ropes, making it easier to lift.

3. What are the two types of pulleys?

The two types of pulleys are fixed pulleys and movable pulleys. A fixed pulley is attached to a structure and only changes the direction of the force. A movable pulley is attached to the object being lifted and also provides a mechanical advantage by reducing the force needed to lift the object.

4. How do two masses on a pulley affect each other?

When two masses are connected by a pulley, they are affected by each other's weight. The heavier mass will pull down on the rope, causing the lighter mass to be lifted. This creates a system of balanced forces, where the tension in the rope is equal on both sides of the pulley.

5. What is the equation for calculating the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system can be calculated by dividing the output force (the weight of the object being lifted) by the input force (the force applied to the rope). The equation is MA = Output force / Input force.

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