# Dependent motion problem with ropes

• theBEAST
In summary, the conversation is about solving a problem with two unknowns and finding the rate of change of one variable with respect to another. The person is struggling with setting up the problem and eliminating the constants in the equation using calculus.
theBEAST

## Homework Statement

I attached the problem with my attempt.

The problem I have is that I have two unknowns. I think my set up is wrong. Does anyone know where to put the datum/set up this question?

Thanks!

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• photo (3).jpg
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theBEAST said:

## Homework Statement

I attached the problem with my attempt.

The problem I have is that I have two unknowns. I think my set up is wrong. Does anyone know where to put the datum/set up this question?

Thanks!

What are your two unknowns? Remember, you're looking for dependencies between certain length changes.

gneill said:
What are your two unknowns? Remember, you're looking for dependencies between certain length changes.

I know it's A and C but I don't know how to get rid of B :S

theBEAST said:
I know it's A and C but I don't know how to get rid of B :S

Here's your drawing with the distances labeled.

L = SA - SB + 2SC

What you're looking for is the rate of change of SA with respect to a rate of change of SC. So rearrange your formula to have SA on the left and the rest on the right. Now, are you familiar with calculus (derivatives)?

#### Attachments

• Fig1.gif
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gneill said:
Here's your drawing with the distances labeled.

L = SA - SB + 2SC

What you're looking for is the rate of change of SA with respect to a rate of change of SC. So rearrange your formula to have SA on the left and the rest on the right. Now, are you familiar with calculus (derivatives)?

Oh... I see, so if you take the derivative Sb and L are eliminated since they are constant?

theBEAST said:
Oh... I see, so if you take the derivative Sb and L are eliminated since they are constant?

Yup.

## 1. What is a dependent motion problem with ropes?

A dependent motion problem with ropes is a physics problem that involves two or more objects connected by a rope. The motion of one object is dependent on the motion of the other object due to the rope connecting them.

## 2. How do you solve a dependent motion problem with ropes?

To solve a dependent motion problem with ropes, you need to analyze the forces acting on each object and apply Newton's laws of motion. You also need to consider the tension in the rope and how it affects the motion of the objects.

## 3. What are some common examples of dependent motion problems with ropes?

Some common examples of dependent motion problems with ropes include a person climbing a rope, a pulley system, and a swing set. In all of these examples, the motion of one object is dependent on the motion of the other object due to the rope connecting them.

## 4. How does the length of the rope affect the motion in a dependent motion problem?

The length of the rope can affect the motion in a dependent motion problem by changing the tension in the rope. A longer rope will have a higher tension, while a shorter rope will have a lower tension. This can impact the acceleration and velocity of the objects involved.

## 5. What are some common mistakes when solving a dependent motion problem with ropes?

Some common mistakes when solving a dependent motion problem with ropes include forgetting to consider the tension in the rope, not properly identifying the forces acting on each object, and not applying Newton's laws correctly. It is also important to pay attention to the direction of the forces and motions involved in order to get an accurate solution.

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