Pulley/Rotational Torque Problem

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In summary, In Fig. 11-42, there are two blocks with masses of 500 g and 460 g respectively, and a pulley with a radius of 5.00 cm. The heavier block falls 81.4 cm in 2.59 s without the cord slipping on the pulley. The problem involves finding the magnitude of the block's acceleration, the tension in the part of the cord supporting both blocks, the pulley's angular acceleration, and its rotational inertia. To solve this problem, use rotational motion equations and the concept of inertia.
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mastermike707
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Homework Statement


In Fig. 11-42, one block has a mass M = 500 g, the other has mass m = 460 g, and the pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 81.4 cm in 2.59 s (without the cord slipping on the pulley).

(a) What is the magnitude of the block's acceleration?

(b) What is the tension in the part of the cord that supports the heavier block?

(c) What is the tension in the part of the cord that supports the lighter block?

(d) What is the magnitude of the pulley's angular acceleration?

(e) What is its rotational inertia?
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The Attempt at a Solution



I am completely confused and I don't even know how to start this problem. Please help!

I tried doing .814=1/2a*2.59^2 to find a and it is wrong. :(
 
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  • #2
It is a rotational motion problem because of the inertia of the pulley.
Use torque = (moment of inertia)*(angular acceleration)
 
  • #3
How do I find the magnitude of the block's acceleration?

I am pretty sure it has something to do with the heavier block falling .814 meters in 2.59 seconds
 
  • #4
Use an accelerated motion formula such as d = Vi*t + .5a*t^2
 

FAQ: Pulley/Rotational Torque Problem

1. What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or cable that runs through the groove. It is used to lift or move objects by applying a downward force on one end of the rope and pulling the other end.

2. How does a pulley work?

A pulley works by distributing the weight of an object equally among multiple ropes or cables. This reduces the amount of force needed to lift the object, making it easier to move. The more pulleys that are used, the less force is required to lift the object.

3. What is rotational torque?

Rotational torque, also known as torque, is a measure of the force that causes an object to rotate around an axis. It is the product of the force applied and the distance from the axis of rotation. In pulley systems, the torque is the force applied to the rope multiplied by the radius of the pulley.

4. How do pulleys affect rotational torque?

Pulleys can affect rotational torque by changing the direction of the force applied to an object. In a simple pulley system, the force applied to the rope is redirected, causing the torque to be distributed among multiple ropes. This reduces the overall torque needed to lift the object.

5. What are some real-world applications of pulley/rotational torque problems?

Pulley/rotational torque problems are commonly encountered in everyday life, such as in elevators, cranes, and exercise equipment. They are also used in industrial settings, such as in manufacturing processes and construction. Additionally, pulleys and rotational torque are important concepts in engineering and physics, and are essential in understanding how machines and structures operate.

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