# Solve Mass Homework w/ Pullys: Is it Uniform?

• viciousp
In summary, by using the equations for force, torque, and moment of inertia, you determined that the pulley is not uniform based on the different values for moment of inertia.
viciousp

## Homework Statement

You've been given a pulley for your birthday. It is a fairly big pulley 12 cm in diameter and with mass 2kg. You get to wondering if the pulley is uniform. To find out, you hang a 1kg textbook 1.0 meters above the floor and use a stopwatch to measure the time it takes it to fall (.71 seconds). What can you conclude about the pully

## Homework Equations

t= r x F
t = I$$\alpha$$
F= ma

## The Attempt at a Solution

I solved for the acceleration of the books

1.0 = .5a(.71)^2
a= 3.97 m/s^s

Then used force equation on the book with a mg down and T up (axises are pointing down and to the right)

mg- T = ma
T= m(g-a) = 5.83N

Since the tension is equal to the force of on the pully I used it to find the torque on the pully

t= r x F
t=(.06)(5.83) = .350 N*m

I used to the torque to solve for Moment of Inertia using the other torque equation

t= I( a/r)
t(r/a)= I = .0053 kg*m^2

Then I solved for Moment of Inertia of a uniform disk
I= 1/2Mr^2
I=.5(2)(.06)^2 = .0036 kg * m^2

Since the two moments on inertia are not the same the pully is not uniform. Is that correct?

Your calculation is correct.

I would say that your approach and calculations are correct. Based on your calculations, the moment of inertia for the pulley is not equal to the moment of inertia for a uniform disk of the same mass and radius. This suggests that the pulley is not uniform. However, to confirm this conclusion, it would be beneficial to repeat the experiment with different masses and distances to ensure accuracy and consistency in the results. Additionally, checking for any other factors that may affect the results, such as friction or air resistance, would also be important. Overall, your approach and conclusion are valid, but further experimentation and analysis may be needed for a more conclusive answer.

## 1. What is the purpose of using pulleys in mass homework?

Pulleys are used in mass homework to demonstrate the principles of uniform motion and how forces are distributed when using pulleys. They also help students understand the concepts of work and mechanical advantage.

## 2. How do pulleys affect the mass being moved?

Pulleys distribute the weight of the mass evenly along the rope or cable, making it easier to lift or move the mass. This is known as uniform motion, where the mass moves at a constant speed and the tension in the rope is equal on both sides of the pulley.

## 3. Do all pulleys create uniform motion?

No, not all pulleys create uniform motion. The pulleys used in mass homework are designed specifically to create uniform motion by distributing the weight of the mass evenly. Other types of pulleys, such as fixed pulleys, do not create uniform motion.

## 4. Can the number of pulleys affect uniform motion?

Yes, the number of pulleys used can affect uniform motion. Adding more pulleys can decrease the amount of force needed to lift or move a mass, but it does not change the uniform motion created by the pulleys.

## 5. How can pulleys help us in real-life situations?

Pulleys are used in many real-life situations, such as elevators, cranes, and even in simple tasks like opening and closing blinds. They help distribute weight and make it easier to lift or move heavy objects, reducing the amount of force needed by the user.

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