# How do I calculate mass of pulley and force of friction on AtwoodMach.

• francisco300
In summary: Then check the equations are right, then check the arithmetic.In summary, the conversation discusses calculating the mass of a pulley and the force of friction using collected data. The equations used involve the net mass, acceleration, and force, and the conversation also mentions the use of a sensor to collect data. There is a discrepancy in the final calculation, which may be due to incorrect equations or arithmetic. The conversation ends with a reminder to double-check the equations being used.
francisco300

## Homework Statement

Basically, I need to calculate the mass of the pulley and friction using data that I collected.

## Homework Equations

I was given: (m1 - m2)g = (m1 + m2 + mp)a + f

## The Attempt at a Solution

For the first part, I collected data using a sensor to find the acceleration. I kept the total mass attached to each cup on each side of the machine constant but changed the difference in their masses by 10g each run.

After 6 runs, I plotted my data of Fnet vs Acceleration. Fnet is (m1 - m2)g (I converted g into dynes). When I get my slope, the lab manual says that i should "expect our plot of (m1 - m2)g vs a to have a slope larger than (m1 - m2)g by an amount equal to the effective mass of the pulley mp and a positive intercept equal to the frictional force f"

My equation turned out to be y = 143.28x + 323.24 (i used best fit line).

This means 143.28 = m1 + m2 + mp
In which case mp= 28.5g right?

Then the force of friction should = 323.4 right?
Is the unit in dynes?

For part b, did the same procedure but kept the net force constant instead of the total mass. I gathered my data and plotted

1/a vs m1 + m2

I got y = 0.0002x + 0.0059 as my best fit line

Now I have to use this equation to find the force of friction

1/a = ((m1 + m2) )/((m1-m2)g-f) + mp/((m1-m2)g-f)

But i get 4950 which I believe is in Netwons and that would be too much considering 323 dynes = 0.00323 Newtons

#### Attachments

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You seem to be working the equations correctly - they may be the wrong equations of course, so you should check that you understand them. Don't just assume they are right: check!

The first thing you need to do is check those units - do that by dimensional analysis.

## 1. How do I calculate the mass of a pulley in an Atwood Machine?

In order to calculate the mass of a pulley in an Atwood Machine, you will need to first measure the radius of the pulley and the distance between the center of the pulley and the point where the string is attached. Then, use the formula M = r^2 * I / (2 * h), where M is the mass of the pulley, r is the radius of the pulley, I is the moment of inertia, and h is the distance between the center of the pulley and the point where the string is attached.

## 2. How can I determine the force of friction on an Atwood Machine?

The force of friction on an Atwood Machine can be determined by first measuring the mass of the pulley and the hanging masses. Then, use the formula F = (m1 - m2) * g, where F is the force of friction, m1 is the mass on one side of the pulley, m2 is the mass on the other side of the pulley, and g is the acceleration due to gravity.

## 3. What is an Atwood Machine and how does it work?

An Atwood Machine is a simple machine that consists of a pulley, string, and two masses hanging on either side of the pulley. The two masses are connected by a string that passes over the pulley. When one mass is heavier than the other, the system will accelerate as the heavier mass falls and the lighter mass rises. This machine is used to demonstrate concepts of tension, friction, and acceleration.

## 4. How is tension calculated in an Atwood Machine?

Tension in an Atwood Machine can be calculated by using the formula T = m * a, where T is the tension in the string, m is the mass of the hanging mass, and a is the acceleration of the system.

## 5. Are there any assumptions that need to be made when calculating the mass of a pulley and force of friction on an Atwood Machine?

Yes, when calculating the mass of a pulley and force of friction on an Atwood Machine, it is assumed that the system is in equilibrium (i.e. not accelerating) and that the pulley and string are massless. Additionally, the force of friction is assumed to act only in the direction opposite of the motion of the masses.

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