# What is the magnitude of acceleration in a system with two boxes and a pulley?

In summary, the conversation is discussing a physics problem involving two boxes and a pulley. The boxes have the same mass and the system is accelerating downwards. The problem asks to calculate the magnitude of the acceleration. The solution involves using torque and the equation Td-Tu=I alpha/r, which simplifies to a=g/2.5. The error in the calculation was due to using the incorrect value for acceleration due to gravity, which led to getting 3.5 instead of the correct answer of 4.

## Homework Statement

http://img148.imageshack.us/img148/8686/ssslk.png
the two boxes and the pulley have the same mass
I=.5mr^2
the system is accelerating downwards calculate the magnitude of the acceleration

## The Attempt at a Solution

I will call the falling one D and the higher one U

mg-Td=ma
Td=mg-ma
Tu=ma
by torque
Td-Tu=I alpha/r
Td-Tu=I a/r^2
Td-Tu=(.5mr^2) a/r^2
Td-Tu==.5ma
mg-ma-ma=.5ma
2.5a=g
a=g/2.5=3.5
what's wrong here??
in the exam I got 4 out of 5 in this question I can't see why I didnt get a full mark I revised everything

Last edited by a moderator:
a=g/2.5=3.5

Try doing this part again

Remember: g=9.81m/s2

uh lol so after all that work my error was numerical serves me right for using my head and not the calculator in this exam because I thought it was an easy division they should have only subtracted a half -.-

## 1. What is the purpose of a pulley in a two-box system?

A pulley is used in a two-box system to change the direction of the force needed to lift an object. It allows for a downward force to be converted into an upward force, making it easier to lift the object.

## 2. How does the weight of the boxes affect the system?

The weight of the boxes affects the system by determining the amount of force needed to lift them. The heavier the boxes, the more force is required to lift them. This force is shared between the two sides of the pulley, making it easier to lift the boxes.

## 3. Can the direction of the pulley affect the system?

Yes, the direction of the pulley can affect the system. If the pulley is facing away from the object being lifted, it will require more force to lift. If the pulley is facing towards the object, it will require less force to lift. This is because the direction of the pulley changes the direction of the force needed to lift the object.

## 4. How does friction impact the efficiency of the system?

Friction can impact the efficiency of the system by creating resistance and reducing the amount of force that is transferred through the pulley. This can result in a decrease in the overall efficiency of the system and make it more difficult to lift the object.

## 5. What are some real-world applications of a two-box and pulley system?

Two boxes and a pulley systems are commonly used in elevators, construction, and transportation industries. They are also used in simple machines, such as cranes and hoists, to lift heavy objects. This system is also used in mountain climbing and rescue operations to help lift individuals and equipment to higher elevations.

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