# Dependent motion with ropes question

• JustinLiang
The person is struggling with a problem and is not sure if they are using the correct geometry. They mention taking the flip Va/V and getting the right answer. They also talk about using the method of Sa + Sb = L1 and taking the time derivative to find Va. They mention that as X increases at a rate of 1.5 m/s, both SA and theta change and that V=VA is not true. They are asked to find the derivative of YB with respect to time in terms of X.In summary, the person is having trouble with a problem and is unsure if their geometry is correct. They mention using the flip Va/V and the method of Sa + Sb = L1 to find Va.
JustinLiang

## Homework Statement

I attached the problem with my attempt. I think the geometry I used is correct but I am getting the wrong answer. When I take the flip Va/V (as shown in my attempt) I get the right answer. I am not even sure if I can relate velocity with a triangle.

The method I used is based on the fact that Sa + Sb = L1 so when you take the time derivative you get Va = -Vb.

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X=SA cos(theta). As X increases in the rate of 1.5 m/s, both SA and theta change. It is not true that V=VA.

Write out YB in terms of X, and find the derivative with respect the time. ehild

## 1. What is dependent motion with ropes?

Dependent motion with ropes refers to the movement of objects that are connected by a rope or string. The motion of one object is affected by the motion of the other object due to the tension in the rope.

## 2. How is dependent motion with ropes different from independent motion?

In independent motion, the movement of one object is not affected by the movement of another object. However, in dependent motion with ropes, the movement of one object is influenced by the movement of another object due to the tension in the rope connecting them.

## 3. What is the formula for calculating the tension in a rope in dependent motion?

The formula for calculating tension in a rope in dependent motion is T = m1a1 + m2a2, where T is the tension, m1 and m2 are the masses of the objects connected by the rope, and a1 and a2 are their respective accelerations.

## 4. How does the angle of the rope affect dependent motion?

The angle of the rope affects dependent motion by changing the direction of the tension force. When the angle is larger, the tension force will be smaller and the objects will move slower. When the angle is smaller, the tension force will be larger and the objects will move faster.

## 5. Can you give an example of dependent motion with ropes in real life?

Yes, a common example of dependent motion with ropes is a person using a pulley system to lift a heavy object. The person applies a force to one end of the rope, causing tension in the rope and causing the object to move upwards. The movement of the object is dependent on the movement of the person pulling the rope.

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