Solve Step Pulley System Homework: Acceleration Relation

In summary, a step pulley system is a mechanical system that uses pulleys with different diameters to transfer motion and power between shafts. The acceleration in this system is affected by the difference in diameter between the pulleys, and can be calculated using a specific formula. The acceleration relation is based on the ratio of pulley diameters, and using a step pulley system has advantages such as variable speed and torque, simplicity, and ease of maintenance and repair.
  • #1
RaikkoBoy7
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Homework Statement


A step Pulley system is shown in the figure.The string and Pulley are of Negligible Mass.The relation Between the acceleration of Block and Block will be what then ?I am having troubles in approaching this question!


Homework Equations





The Attempt at a Solution

 

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  • #2
What did you try?
 
  • #3
Ratio of their tension 1:2 and Ratio of tension=ratio of acceleration=1:2
But the answer is 1:4
 

1. What is a step pulley system?

A step pulley system is a mechanical system that uses a series of pulleys with different diameters to transfer motion and power from one shaft to another. The pulleys are connected by a belt, and the system allows for varying levels of speed and torque.

2. How does the step pulley system affect acceleration?

The acceleration in a step pulley system is affected by the difference in diameter between the pulleys. The larger the diameter of the driving pulley compared to the driven pulley, the greater the acceleration will be. This is because a larger diameter pulley requires the belt to travel a greater distance in a shorter amount of time.

3. What is the acceleration relation in a step pulley system?

The acceleration relation in a step pulley system is based on the ratio of the diameters of the pulleys. The acceleration of the driven pulley is equal to the acceleration of the driving pulley multiplied by the inverse of the ratio of the pulley diameters. This means that the smaller the driven pulley is compared to the driving pulley, the greater the acceleration will be.

4. How is the acceleration calculated in a step pulley system?

The acceleration in a step pulley system can be calculated using the formula: a = (Rd/Rd+1) x Ad, where "a" is the acceleration, "Rd" is the driven pulley diameter, and "Ad" is the driving pulley diameter. This formula is based on the acceleration relation in a step pulley system.

5. What are the advantages of using a step pulley system?

One advantage of using a step pulley system is that it allows for variable speed and torque without the need for complex machinery. It is also a simple and cost-effective way to transfer motion and power between shafts. Additionally, step pulley systems are relatively easy to maintain and repair, making them a popular choice in many industries.

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