# Understanding the Motion of Double Pulleys: Exploring Acceleration and Forces

• Carbon123
In summary, the conversation discusses finding the accelerations of three masses, m1, m2, and m3, connected by a pulley system. The equations of motion used in the solution involve taking upward as the positive direction for each of the masses, and the accelerations are relative to the earth. The direction of movement for m1 depends on the value of a1, which is equal to negative of the sum of a2 and a3 divided by 2.
Carbon123

## Homework Statement

A mass m1 is hung on a pulley with another pulley on th eother side with two masses;m2 and m3.Find the accelerations of the masses

F=M.a
a1=-(a2+a3)/2

## The Attempt at a Solution

So in my book ,the solution provided was 2T-m1g=m1a1
T-m2g=m2a2 and T-m3g =m3a3.My question is why did the two equations for mass 2 and mass 3 seems to have both objects to move upwards,shouldn't one move down and one up ?why is the equation of motion like that ?

The book is apparently taking upward as the positive direction for each of the three masses when setting up ΣF = ma.

The accelerations in the equations are accelerations relative to the earth.
m2 and m3 do not necessarily move in opposite directions relative to the earth.

But what about m1 which is also 2T-m1g=m1a1 wouldn't that imply that it moves upward and thus the two mass m2 and m3 moves downward relative to the Earth ?(or is it because the a1 is equal to negative a2+a3/2?

Assuming the masses are released from rest, if a1 turns out to be a positive number then m1 moves upward. If a1 turns out to be negative then m1 moves downward.

## What is a double pulley problem?

A double pulley problem is a physics problem that involves two pulleys connected by a single belt or rope. The goal of the problem is to determine the mechanical advantage and the force required to move an object using the pulley system.

## How do you calculate the mechanical advantage of a double pulley system?

The mechanical advantage of a double pulley system is calculated by dividing the weight of the object being lifted by the force applied to the rope or belt. This ratio is also known as the ideal mechanical advantage (IMA) and can be used to determine the efficiency of the pulley system.

## What is the difference between fixed and movable pulleys in a double pulley system?

In a double pulley system, the fixed pulley is attached to a stationary object, while the movable pulley is attached to the object being lifted. The fixed pulley changes the direction of the force, while the movable pulley reduces the amount of force needed to move the object.

## How does friction affect the mechanical advantage of a double pulley system?

Friction can decrease the mechanical advantage of a double pulley system by reducing the efficiency of the pulleys. The friction between the rope or belt and the pulleys can cause some of the applied force to be lost, resulting in a lower mechanical advantage.

## What are some real-life applications of double pulleys?

Double pulleys are commonly used in construction, elevators, and weightlifting equipment. They can also be found in everyday objects such as window blinds and flagpoles. Double pulleys allow for heavy objects to be lifted with less force, making tasks easier for humans.

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