# Pulley w/ 3 Masses Homework: Find Linear Acceleration

• aszymans
In summary, the conversation discusses a physics problem involving a system of objects with different masses and radii. The system is released from rest and the question asks for the magnitude of the linear acceleration of a hoop. There is also a mention of using a massless pulley in the solution.

## Homework Statement

An green hoop with mass mh = 2.4 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.4 kg and radius Rd = 0.11 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.2 kg and radius Rs = 0.25 m. The system is released from rest.

1)What is magnitude of the linear acceleration of the hoop?

## The Attempt at a Solution

I have no idea, would love someone to explain all the very elementary steps, we have never even looked at taking the mass of the pulley into account!

How would you solve it if the pulley were massless?

## What is a pulley with 3 masses?

A pulley with 3 masses is a simple machine consisting of a wheel and a rope or belt that is used to lift or move objects. The pulley has 3 masses attached to it, which can either be on the same side of the pulley or on opposite sides.

## How does a pulley with 3 masses work?

A pulley with 3 masses works by using the principle of mechanical advantage. When one end of the rope is pulled, the pulley rotates, and the weight of the masses on one side is transferred to the other side. This reduces the amount of force needed to lift the load, making it easier to move.

## What is linear acceleration?

Linear acceleration is the rate of change of an object's velocity in a straight line. It is a measure of how quickly the object is speeding up or slowing down. In the context of a pulley with 3 masses, linear acceleration refers to the change in speed of the moving masses as they are lifted or lowered by the pulley.

## How do you calculate linear acceleration in a pulley with 3 masses?

To calculate linear acceleration in a pulley with 3 masses, you need to know the masses of the objects, the tension in the rope, and the radius of the pulley. You can then use the formula a = (m1 – m2)g / (m1 + m2 + m3), where a is the linear acceleration, m1-m3 are the masses, and g is the acceleration due to gravity.

## What are the practical applications of a pulley with 3 masses?

Pulleys with 3 masses have various practical applications, such as in elevators and cranes, where they are used to lift heavy loads. They are also commonly used in weightlifting equipment and in the construction of bridges and buildings. Additionally, pulleys with 3 masses are essential components in many mechanical systems, making it easier to move objects and machinery.