# Solve Pulley-Mass System: m1=4.00 kg, m2=1.00 kg

• Taniaz
In summary, the problem involves two masses, m1 and m2, connected by a massless and frictionless pulley system. The goal is to determine the acceleration of each mass, given that m1=4.00 kg and m2=1.00 kg and the surface is frictionless and horizontal. The equations used to solve the problem are T1=m1a1 and w2-T2=m2a2 for mass m1 and pulley 2T1=T2. The pulley is not attached to anything and is hanging by the string, causing the attached mass to move up or down according to its acceleration. The acceleration of a1 is twice that of a2, which can be determined by differentiating
Taniaz

## Homework Statement

The pulleys in the figure (attached) are massless and frictionless, determine the acceleration of eah of m1 and m2, given that m1=4.00 kg, and m2=1.00 kg, and the surface is frictionless and horizontal.

## Homework Equations

For mass m1: T1=m1a1 and mass m2: w2-T2=m2a2
For the pulley 2T1=T2

## The Attempt at a Solution

I don’t understand how the mass m2, which is hanging, is moving. Why is it moving downwards? If m1 is moving to the right, then shouldn’t the pulley move anticlockwise and pull m2 upwards?
How is it attached?
How is the pulley making it move upwards or downwards if it’s attached to the center of the pulley?
How is the acceleration of a1=2a2?

Thank you

#### Attachments

• F4C1FE86-0816-4958-A55D-671DFCA7D8E4.jpeg
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Taniaz said:
If m1 is moving to the right, then shouldn’t the pulley move anticlockwise and pull m2 upwards?
No. I suggest that you write down an equation for the total length of the string as the sum of the length of all parts of the string and differentiate it with respect to time. Since the string length is fixed, this time derivative should be zero. Also, you should specify which pulley you are talking about.

Taniaz said:
How is it attached?
Assuming that you are talking about the lower right pulley, it is not attached to anything. It is hanging by the string.

Taniaz said:
How is the pulley making it move upwards or downwards if it’s attached to the center of the pulley?
The pulley itself will move up or down and so the mass attached to it will do so as well.

Taniaz said:
How is the acceleration of a1=2a2?
This should follow after you differentiate the total length of the string (which I told you to write down in the first hint) a second time.

Got it, thank you!

## 1. What is a pulley-mass system and how does it work?

A pulley-mass system is a mechanical system that uses one or more pulleys and masses to transfer and balance forces. The pulley serves as a simple machine that changes the direction of the applied force and can also increase or decrease the magnitude of the force. In this system, the masses are connected by a rope or cable that runs over the pulley(s). As one mass moves, the other mass will move in the opposite direction.

## 2. What is the equation for solving a pulley-mass system?

The equation for solving a pulley-mass system is F = ma, where F is the net force acting on the system, m is the total mass of the system, and a is the acceleration of the system. This equation is based on Newton's Second Law of Motion, which states that the net force on an object is equal to its mass multiplied by its acceleration.

## 3. How do you calculate the acceleration of a pulley-mass system?

To calculate the acceleration of a pulley-mass system, you must first determine the net force acting on the system. This can be done by considering the forces acting on each mass, including the force of gravity (weight) and any applied forces. Once you have the net force, you can use the equation F = ma to solve for the acceleration. Keep in mind that the acceleration will be the same for both masses in the system.

## 4. What are the units for the masses in a pulley-mass system?

The units for the masses in a pulley-mass system are typically kilograms (kg) in the metric system or pounds (lbs) in the imperial system. It is important to use consistent units when solving these types of problems.

## 5. How do you determine the tension in the rope or cable of a pulley-mass system?

To determine the tension in the rope or cable of a pulley-mass system, you can use the equation T = mg, where T is the tension, m is the mass of the object being lifted, and g is the acceleration due to gravity (9.8 m/s^2 on Earth). This equation assumes that the rope or cable is massless and there is no friction in the system. If friction is present, the tension will be slightly higher than calculated using this equation.

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