Mechanics - Pulley system finding coefficient of friction

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Homework Help Overview

The discussion revolves around a mechanics problem involving a pulley system where the goal is to determine the minimum coefficient of friction required to prevent a farmer from slipping. The participants are exploring the relationships between forces acting on the farmer, including tension, normal force, and friction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of free body diagrams to analyze forces acting on the farmer, including tension and normal force. There are attempts to clarify how to derive the minimum static friction from the equations provided, with some questioning the definitions and relationships between the forces involved.

Discussion Status

Some participants have offered guidance on constructing free body diagrams and balancing forces, indicating a productive direction in the discussion. However, there is no explicit consensus on the approach to finding the minimum friction, and participants continue to express uncertainty about the equations and their application.

Contextual Notes

There is mention of specific values and angles in the problem, but the discussion highlights a lack of clarity regarding the direction and magnitude of forces, as well as the need for a general equation to find the normal force.

Roaku
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Homework Statement


Mechanics Q36a.png



Homework Equations



I believe:
F = m . a
Ffriction = μs . N
Ffriction = μs . mg . cosθ

The Attempt at a Solution


I don't quite get how the equations above would give me an answer to the minimum friction required so that the farmer doesn't slip. I know Fl = (70x9.81)cos(40) = 526N But there is now a variable Ffriction that I don't know how to find...

I'm terrible at physics. If someone could explain or give me a head start, it would be appreciated.
 
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Hi Roaku! Welcome to PF :smile:

Start by making the free body diagram of the problem. You will have the forces balanced as, for the vertical direction, of the farmer...

Tsin\theta - mg = N

where N is the normal reaction, and T is tension in the rope.

Similarly, you will have an equation for the horizontal direction for the farmer, involving frictional force. Find the normal reaction from the above equation and use it in the one you made to get the minimum static friction.
 
Roaku said:

Homework Statement


View attachment 48197


Homework Equations



I believe:
F = m . a
Ffriction = μs . N General Equatiom
Ffriction = μs . mg . cosθ NOT general equation

The Attempt at a Solution


I don't quite get how the equations above would give me an answer to the minimum friction required so that the farmer doesn't slip. I know Fl = (70x9.81)cos(40) = 526N But there is now a variable Ffriction that I don't know how to find...

I'm terrible at physics. If someone could explain or give me a head start, it would be appreciated.

Use only general equation.
Then find value of N.
You also need to know not only the magnitude but also the direction of all the forces involve.
 
Last edited:
Infinitum said:
Start by making the free body diagram of the problem. You will have the forces balanced as, for the vertical direction, of the farmer...

Tsin\theta - mg = N

where N is the normal reaction, and T is tension in the rope.

The free-body diagram refers to the man. N is the normal force exerted on his feet by the ground. It points upward. The ground can not exert downward force. The vertical component of the tension also points upward. The weight of the man points downward. So the equation for the vertical force components is Tsin(theta)+N-mg=0, that is, N= mg-Tsin(theta)

ehild
 
Whoops, I mis-posted the equation.

Tsin\theta - mg + N = 0

Thanks for observing that, ehild :smile:
 

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