# Dynamics, dependent motion analysis

• mathmannn
In summary, the question deals with finding the velocity of block B after it moves 0.5 m from its original position, when connected to a massless pulley along with block A (50 kg) and starting from rest. The solution shows that the vectors for v_A and v_B are in opposite directions, but the statement v_A = v_B could be referring to the magnitudes of the velocities. The professor may have chosen a coordinate system where both blocks move in the same direction, with one moving down (positive direction) and the other moving up (positive direction). This allows for a consistent direction of motion for both objects.
mathmannn

## Homework Statement

All of this is in the attachment, but here is the question anyways.

"Two blocks of masses A, 50 kg and B, 30 kg are connected to a mass*less pulley which is connected to a wall. Determine the velocity of block B after it moves 0.5 m from its original position. Assume no friction and that the blocks start from rest"

## The Attempt at a Solution

Obviously, I don't need help finding a solution but I can not wrap my head around how my professor got the relationship that $v_A = v_B$. I see that the length of the movement of one block is equal to the other, but why do they have the same sign?

If we define the positive x-axis to be in the direction that block A moves "down" (towards the right) then block B would move "up" so their position and their velocities would have to be opposite of each other?

Can anyone explain to help me see what is going on?

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mathmannn said:

## Homework Statement

All of this is in the attachment, but here is the question anyways.

"Two blocks of masses A, 50 kg and B, 30 kg are connected to a mass*less pulley which is connected to a wall. Determine the velocity of block B after it moves 0.5 m from its original position. Assume no friction and that the blocks start from rest"

## The Attempt at a Solution

Obviously, I don't need help finding a solution but I can not wrap my head around how my professor got the relationship that $v_A = v_B$. I see that the length of the movement of one block is equal to the other, but why do they have the same sign?

If we define the positive x-axis to be in the direction that block A moves "down" (towards the right) then block B would move "up" so their position and their velocities would have to be opposite of each other?

Can anyone explain to help me see what is going on?

The solution clearly shows that the vectors for v_A and v_B are in opposite directions (I'm talking about the arrows in the diagram).

The statement v_A = v_B could have been referring to the magnitudes of the velocities. After all, there are no vector arrows over the symbols for the quantities, suggesting that they are meant to be scalars.

As a general rule, you define the direction of motion of any object to be the positive direction. Imagine if you unwound the string from around the pulley and laid the two blocks out on a flat surface. In that case you would clearly see that pulling on one block makes them both move in the same direction.
Your professor chose a coordinate system that would result in a consistent direction of motion for both objects. If one block moves down (positive direction) the other one must move up (positive direction).

cheers

## 1. What is dynamics and dependent motion analysis?

Dynamics is the branch of physics that studies the motion of objects and the forces that cause that motion. Dependent motion analysis is a method of analyzing the motion of multiple objects that are connected or dependent on each other.

## 2. What types of forces are involved in dependent motion analysis?

The forces involved in dependent motion analysis are typically tension, normal force, friction, and gravity. These forces can also be broken down into their components, such as horizontal and vertical forces.

## 3. How do you determine the acceleration of objects in dependent motion analysis?

To determine the acceleration of objects in dependent motion analysis, you can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). By analyzing the forces acting on each object and their masses, you can calculate the acceleration.

## 4. Can dependent motion analysis be applied to real-world scenarios?

Yes, dependent motion analysis can be applied to real-world scenarios, such as analyzing the motion of a pulley system or a block sliding down an inclined plane. It is a useful tool for understanding and predicting the motion of objects in various situations.

## 5. What are some practical applications of dependent motion analysis?

Some practical applications of dependent motion analysis include designing and optimizing mechanical systems, such as engines and vehicles, and predicting the motion of objects in engineering and construction projects. It is also used in sports science to analyze the movement of athletes and in video game development to create realistic animations.

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