Related Rates of Accelerations in Pulley Problem

In summary, the conversation revolves around a question regarding a problem from the book "Vector Mechanics for Engineers 10th edition Statics and Dynamics" by Beer. The specific issue is understanding the assumption aC=-1/2aD in part b of sample problem 13.5. The person is seeking help in understanding the solution, which involves applying the equations for uniform and accelerated motion. The conversation ends with a clarification question about the relationship between the motion of points C and D.
  • #1
Alexanddros81
177
4

Homework Statement


Hi!
I am new to this forum and i have problem understanding sample problem 13.5 from Vector Mechanics for Engineers 10th edition Statics and dynamics. (Beer)
In particular I don't understant in part b how he comes to the assumption aC=-1/2aD

If anyone can help
thanks

Homework Equations


Uniform motion: ∑Fy=0
Accelerated Motion: ∑Fy=ma

The Attempt at a Solution


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  • #2
Alexanddros81 said:
In particular I don't understant in part b how he comes to the assumption aC=-1/2aD
If D raises by one unit of distance, by how many units must C lower? (Take a piece of string and play with it.)
 

Related to Related Rates of Accelerations in Pulley Problem

What is the concept of related rates of accelerations in pulley problem?

The concept of related rates of accelerations in pulley problem involves the study of how the acceleration of an object changes in relation to the acceleration of another object connected by a pulley system. This is important in understanding the dynamics and motion of objects in pulley systems.

How do you solve related rates of accelerations in pulley problem?

To solve related rates of accelerations in pulley problem, you need to first identify the variables involved, such as the masses of the objects, the length of the rope, and the accelerations of the objects. Then, you can use the equations of motion and the relationships between the variables to set up an equation and solve for the unknown acceleration.

What are some common applications of related rates of accelerations in pulley problem?

Related rates of accelerations in pulley problem is commonly used in engineering and physics, particularly in the design and analysis of pulley systems. It is also relevant in understanding the motion of everyday objects, such as elevators and cranes, which use pulley systems for lifting and lowering.

What are some challenges in solving related rates of accelerations in pulley problem?

One of the main challenges in solving related rates of accelerations in pulley problem is the complexity of the pulley system itself. The number of objects and ropes involved, as well as their masses and accelerations, can make the problem difficult to visualize and solve. Additionally, the motion of the objects may not be linear, which adds another layer of complexity.

How can understanding related rates of accelerations in pulley problem benefit us?

Understanding related rates of accelerations in pulley problem can help us make more accurate predictions and calculations in a variety of real-world scenarios. It also allows us to design and optimize pulley systems for efficiency and safety. Additionally, the problem-solving skills and critical thinking involved in solving these types of problems are valuable in many fields of study and work.

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