# Relative velocity problem with pulleys

• ual8658
In summary, the conversation discusses how to calculate the velocity of block B (Vb) in relation to block A (Va) based on the equation Vb/a = Vb - Va. The individual attempts to solve the problem by using the equation 2(Xa) + (Xb/a)cos15 = constant and taking its derivative. However, they get stuck on how to calculate Vb and ask for clarification on the direction and incline of Vb/a. Another person suggests that Vb is equal to 8.53 at an angle of 14.05 degrees on the block, but their explanation is different from what the book says. In the end, it is clarified that for every inch block A descends along
ual8658

Vb/a = Vb - Va

## The Attempt at a Solution

I got as far as realizing that the velocity of B depends on A so I wrote out:
2(Xa) + (Xb/a)cos15 = constant

and took the derivative of that equation to get Vb/a = -16.56. I then got stuck as to how to get Vb.

Is Vb/a in the direction of the rope pulling on B and would Vb be in that direction too? Also since Vb/a is at an incline, how would i put it into the relative velocity equation to account for two velocities at incline?

Have I missed something here? For every inch that block A descends along the ramp, block B is pulled by 1 inch. This is because the string is of constant length. So B has the same numerical acceleration and speed as A, but acting in the direction of the 15 degree angle as shown. (Velocity and acceleration must be defined in direction).

tech99 said:
Have I missed something here? For every inch that block A descends along the ramp, block B is pulled by 1 inch. This is because the string is of constant length. So B has the same numerical acceleration and speed as A, but acting in the direction of the 15 degree angle as shown. (Velocity and acceleration must be defined in direction).

Well the key says that Vb should be 8.53 at an angle of 14.05 degrees on the block. Your explanation makes much more sense so I don't get why the book would say this.

## 1. What is the relative velocity problem with pulleys?

The relative velocity problem with pulleys is a physics concept that involves calculating the speed and direction of an object in motion based on the movement of two or more pulleys. This problem is commonly used to understand the relationship between the velocities of different objects in a system.

## 2. How does a pulley affect relative velocity?

A pulley affects relative velocity by changing the direction of motion of an object. When a rope or belt is wrapped around a pulley, the direction of the force applied to the object changes, resulting in a change in velocity. This change in velocity can be determined by using the principles of pulley mechanics and vector addition.

## 3. What factors affect the relative velocity problem with pulleys?

The factors that affect the relative velocity problem with pulleys include the size and shape of the pulley, the mass of the objects attached to the pulley, and the tension in the rope or belt connecting the objects. The angle at which the rope or belt is attached to the pulley can also affect the relative velocity.

## 4. How do you solve a relative velocity problem with pulleys?

To solve a relative velocity problem with pulleys, you will need to use the principles of vector addition and the equations of motion. First, draw a diagram of the pulley system and label all known and unknown variables. Then, use the equations of motion to calculate the velocities of the objects in the system. Finally, use vector addition to determine the final velocity and direction of the object of interest.

## 5. Can the relative velocity problem with pulleys be applied to real-world situations?

Yes, the relative velocity problem with pulleys can be applied to real-world situations. This concept is commonly used in engineering and mechanics to design systems that involve pulleys, such as elevators, cranes, and conveyor belts. It is also used in physics experiments and simulations to understand the motion of objects in different scenarios.

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