# Two pulleys and two masses on a slope

• vinamas
In summary, the conversation discusses the arrangement of two masses connected to two pulleys via ropes, with specific masses and angles given. The problem asks for the angular acceleration and linear acceleration of each pulley, as well as the force of the ropes connected to the pulleys. The equations for torque and angular acceleration are mentioned, but the attempt at a solution is difficult to understand due to a lack of clear variables and explanations. A better image or more detailed description of the pulley arrangement is recommended for a clearer understanding of the problem.
vinamas
1. The problem statement, all variables
Use this photo
http://m.imgur.com/a/lQd9q

Two masses are connected to two pulleys via ropes.The mass of the hung mass is 16kg and the mass of the object on the slope is 8kg the slope has an angle of 37 degrees. Pulleys 1 has a mas of 6 kg and Pulley 2 has a mass of 4 kg. using the picture and the given info find the following (the kinetic friction coefficient is 0.23)
a) Angular acceleration for the two pulleys
b) the linear acceleration for each pulley
c) the force of each of the ropes that are connected to the pulley

## Homework Equations

angularacceleration=a/r
Torque=F.r
angularacceleration=Torque/I

## The Attempt at a Solution

angularacceleration=torque/i
((m1g-Ft1)r1-(-Fk-m2g×sin37+Ft2)r2)/(0.5)(6)(0.15)^2+(0.5)(4)(0.1)^2
as you can see I already have 3 variables what should i do?

You should provide a better image, one that is oriented properly, or describe the pulley arrangement in better detail in your text. It's preferable to upload images to PF rather than to some off-site storage area.

vinamas said:
((m1g-Ft1)r1-(-Fk-m2g×sin37+Ft2)r2)/(0.5)(6)(0.15)^2+(0.5)(4)(0.1)^2
That is very hard to decipher. The reader has to reverse-engineer the expressions to figure out what all the variables are and what the numbers represent.
Either use LaTeX or, at the least, use the superscript and subscript buttons provided.
Define all your variables. For the constants, it is better to invent and define variables to represent them, only plugging in numbers at the end. (This has many advantages.) if you must plug in numbers straight away, build the expression up in steps, explaining what you are doing.

gneill

## 1. How do two pulleys and two masses on a slope work together?

Two pulleys and two masses on a slope work together through a system of ropes and pulleys. The two masses are connected by a rope that runs over the two pulleys, creating a mechanical advantage. When one mass moves down the slope, the other mass will move up the slope at the same rate due to the conservation of energy.

## 2. What is the purpose of using two pulleys in this system?

The purpose of using two pulleys in this system is to increase the mechanical advantage. With two pulleys, the load can be distributed between the two ropes, making it easier to move the masses up and down the slope. Additionally, using two pulleys reduces the amount of force needed to move the masses, making it more efficient.

## 3. How does the angle of the slope affect the system?

The angle of the slope affects the system by changing the amount of force needed to move the masses. A steeper slope will require more force to move the masses, while a gentler slope will require less force. Additionally, the angle of the slope can affect the direction of motion for the masses.

## 4. What is the relationship between the masses in this system?

The masses in this system have an inverse relationship. As one mass moves down the slope, the other mass will move up the slope at the same rate. This is due to the conservation of energy in the system. As one mass gains potential energy by moving down the slope, the other mass loses an equal amount of potential energy by moving up the slope.

## 5. Are there any real-life applications of two pulleys and two masses on a slope?

Yes, there are many real-life applications of this system, such as elevators, cranes, and escalators. These systems use pulleys and multiple masses to efficiently move heavy loads. Additionally, this system is used in exercise equipment, such as weight machines, to provide resistance and make the exercises more challenging.

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