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

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.

Gold Member
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.

Homework Helper
Gold Member
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.

Homework Helper
Gold Member
2022 Award
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
Mentor
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).