# Find the unknown mass on a inclined rope pulley system.

• dabbih123
In summary, the conversation discusses the calculation of forces acting on mass B, including the force working against it and the force working with it. The method of using Newton's second law to find the mass of B is suggested, but the individual is unsure of how to proceed and requests a free body diagram for each mass.

#### dabbih123

Homework Statement
I have a mass m(A)=2kg on an incline upwards of 30° connected to a pulley system to another mass m(B)=?. The coefficient of friction is 0.18 and the system has an acceleration of 0.58 m/s^2 in the direction up the slope.

What is mass B?
Relevant Equations
F=ma
Mass of A = 2 kg
Acceleration = 0.58 m/s^2
μ=0.18
Friction force = μm(A)g cos 30
Component of gravity parallel to ramp = m(A)g sin 30
Force pulled down by m(B)= m(B)g
First I calculated the forces that were working against mass B.
m(A)g sin 30 + μm(A)g cos 30 = 12.86 N

The force working with mass B is
m(B)g = 9.8m(B)

I thought I could solve for B using F=ma where 12.86 N = (2kg+m(B))*(0.58), but of course, 12.86 N is just the force required to make the system move not the force at acceleration 0.58 m/s^2.

I am not sure how to continue or even if I am on the right track.

A goes upward. Friction force and gravity on A are downward.
Mass of A multiplied by upward acceleration equals upward force by Gravity on B minus above written downward force.

What sort of a pulley system is this? Can you post an image?

If I understand well, you must find the tension of the rope by applying Newton's second law for mass A. Then by applying Newton's second law for mass B you ll be able to find the mass of B, because you will make an equation with only one unknown, the mass of B.

dabbih123 said:
using F=ma
In that equation, F is the net force on a component and m is the mass of the component.
If the component is A, what forces act directly on A? Note that the gravitational force on B acts on B, not on A.

Delta2
I don't see any free body diagrams. Do you feel that you have advanced to the point where you no longer need to use free body diagrams? Your inability to solve this problem is an indication that you haven't.

Please provide a free body diagram for each of the bodies A and B separately, showing all the forces acting on each (including the rope tension).

## 1. How do I calculate the unknown mass on an inclined rope pulley system?

To calculate the unknown mass on an inclined rope pulley system, you will need to use the formula: M = (m1 * g * sinθ) / (a - (m2/m1) * cosθ). Here, M represents the unknown mass, m1 is the known mass, g is the acceleration due to gravity, θ is the angle of the incline, and a is the acceleration of the system.

## 2. What is the purpose of using an inclined rope pulley system to find unknown mass?

An inclined rope pulley system can help to distribute the weight of the unknown mass over multiple ropes and pulleys, making it easier to measure the mass accurately. It also allows for the use of simple physics principles and equations to calculate the unknown mass.

## 3. What are the factors that can affect the accuracy of the measurement in an inclined rope pulley system?

The accuracy of the measurement in an inclined rope pulley system can be affected by factors such as the friction in the pulley system, the precision of the measuring instruments, and the angle of the incline. It is important to minimize these factors as much as possible to obtain a more accurate measurement.

## 4. Can an inclined rope pulley system be used to measure the mass of any object?

Yes, an inclined rope pulley system can be used to measure the mass of any object as long as the weight of the object can be distributed over multiple ropes and pulleys. However, the accuracy of the measurement may vary depending on the size and weight of the object.

## 5. Are there any safety precautions to consider when using an inclined rope pulley system to find unknown mass?

Yes, it is important to ensure that the ropes and pulleys are in good condition and can support the weight of the object. It is also important to wear appropriate safety gear and to have a clear understanding of the physics principles involved in the measurement. It is recommended to have a trained professional supervise the process to ensure safety.