# Pulley system with spring and car EOM

• tisquared
In Summary, the equation of motion for a system with a pulley and a block is incorrect because the moment of inertia is not at the center of the pulley.
tisquared
Hi all! I am working with a problem that for the life of me am having the hardest time with deriving the equation of motion. I have attached the sketch to give a better representation.

The moment of inertia, J, is at the center of the spring. No friction between car and table and cables do not slip, so no friction there either. The spring is undeformed when the system is in static equilibrium.

This is how far I have gotten so far, but it is wrong:
Summing the moments about the center of the pulley and assuming frictionless surface for the block I get the following expression:
m = mass of block

m*r - F(spring)*R = J*theta-doubledot + m*a(acceleration of block towards x)*r
plugging in F(spring) = k*r*theta and a = r*theta-doubledot I get the following
theta-doubledot + ((k*r*R)/(J+m*r^2))theta - (m*r)/(J+m*r^2)

#### Attachments

• pulley system.pdf
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Last edited:
tisquared said:
Hi all! I am working with a problem that for the life of me am having the hardest time with deriving the equation of motion. I have attached the sketch to give a better representation.

The moment of inertia, J, is at the center of the spring. No friction between car and table and cables do not slip, so no friction there either. The spring is undeformed when the system is in static equilibrium.

This is how far I have gotten so far, but it is wrong:
Summing the moments about the center of the pulley and assuming frictionless surface for the block I get the following expression:
m = mass of block

m*r - F(spring)*R = J*theta-doubledot + m*a(acceleration of block towards x)*r
plugging in F(spring) = k*r*theta and a = r*theta-doubledot I get the following
theta-doubledot + ((k*r*R)/(J+m*r^2))theta - (m*r)/(J+m*r^2)

Welcome to the PF!

I don't see the sketch yet -- try again to post it?

I am so sorry! Got it attached now

Bumping

anyone have any input? I really need some help (

## What is a pulley system with spring and car EOM?

A pulley system with spring and car EOM is a mechanical device that uses a combination of a pulley system and a spring to lift or move a car. The EOM stands for "equation of motion" which is a mathematical representation of the system's movement.

## How does a pulley system with spring and car EOM work?

The system works by using the force of the spring to counteract the weight of the car. The car is attached to a rope or cable that runs through a series of pulleys and is connected to the spring. When the car is lifted, the spring is compressed, storing potential energy. As the car is lowered, the spring releases the energy, helping to lift the car.

## What are the advantages of using a pulley system with spring and car EOM?

One advantage is that it can lift heavy objects with less force. The use of a pulley system reduces the amount of effort needed to lift the car. The spring also helps to distribute the weight of the car evenly, making it easier to lift. Additionally, the pulley system allows for more control and precision in the movement of the car.

## What are some common applications of a pulley system with spring and car EOM?

This system is commonly used in car repair shops to lift cars for maintenance or repairs. It is also used in car manufacturing plants to move cars along the assembly line. In addition, it can be used in construction and other industries that require lifting heavy objects.

## What are some safety considerations when using a pulley system with spring and car EOM?

It is important to make sure that the system is properly installed and maintained. The weight of the car and the force of the spring can cause the system to fail if not used correctly. It is also important to have proper training and supervision when using the system to prevent accidents. Regular inspections and maintenance should also be performed to ensure the system is in good working condition.

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