# Multiple Pulleys and Masses with Friction

• Wara
In summary, the conversation is about solving a physics problem involving multiple pulleys and masses with friction. The participant has provided their solution and is unsure if it is correct. They have used equations and calculations to find values for tension and acceleration, and have asked for verification or corrections.
Wara
Multiple Pulleys and Masses with Friction (Picture Included)

## Homework Statement

http://content.screencast.com/users/Waraa/folders/Snagit/media/2d699ba1-32e0-4d9c-b79f-1a1d85dccd12/03.19.2012-15.49.46.png

I have solved the question but I am still iffy as to whether my solution is correct or not.

## Homework Equations

Let m1 = 10kg.
Let m2 = 20kg.

(1) m1a1 = T1 - μm1g
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

## The Attempt at a Solution

T2 = m2g
T2 = (20kg)(9.8m/s2)
T2 = 196N

T1 = $\frac{T_{2} + μm_{1}g}{2}$
T1 = $\frac{196N + (0.32)(10kg)(9.8m/s^{2})}{2}$
T1 = 113.68N

Sub (3) and (4) into (2)
m2a2 = m2g - T2
m2($\frac{a_{1}}{2}$) = m2g - 2T1

Called this new equation (5).
(5) m2($\frac{a_{1}}{2}$) = m2g - 2T1

(1) m1a1 = T1 - μm1g
(5) m2($\frac{a_{1}}{2}$) = m2g - 2T1

(1) + (5)
m1a1 + m2($\frac{a_{1}}{2}$) = T1 - μm1g + m2g - 2T1
a1(m1 + m2($\frac{1}{2}$) = -μm1g + m2g - T1
a1(10kg + 20kg($\frac{1}{2}$) = -(0.32)(10kg)(9.8m/s2)+(20kg)(9.8m/s2)-113.68N
a1 = 2.5448 m/s2

from (4)
2a2 = a1
a2 = $\frac{a_{1}}{2}$
a2 = $\frac{2.548m/s^{2}}{2}$
a2 = 1.274 m/s2

Therefore, T1 = 113.68N, T2 = 196N, a1 = 2.548 m/s2, and a2 = 1.274 m/s2.

My question is if my solution is correct. Please check and reply back with suggestions or corrections. Thank you so much.

Last edited by a moderator:

## 1. How do multiple pulleys affect the tension and force in a system?

When multiple pulleys are used in a system, the tension and force are reduced. This is because the weight of the mass is distributed among the multiple pulleys, causing the force needed to lift the mass to decrease.

## 2. What is the effect of friction on the motion of masses in a pulley system?

Friction causes a decrease in the efficiency of a pulley system by converting some of the energy into heat. This means that the masses will not accelerate as quickly as they would without friction and the system may not be able to lift as much weight.

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

The mechanical advantage of a pulley system is calculated by dividing the output force by the input force. This can be determined by counting the number of ropes supporting the mass and subtracting one. For example, if a system has 4 ropes supporting the mass, the mechanical advantage would be 4-1=3.

## 4. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a fixed point and changes only the direction of the input force. A movable pulley, on the other hand, is attached to the object being lifted and changes both the direction and magnitude of the input force. This means that a movable pulley has a mechanical advantage of 2, while a fixed pulley has a mechanical advantage of 1.

## 5. How does the number of pulleys affect the mechanical advantage of a system?

The number of pulleys in a system directly affects the mechanical advantage. The more pulleys that are added, the greater the mechanical advantage. This is because each additional pulley reduces the force needed to lift the mass, making the system more efficient.

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