Mechanics - Pulley system finding coefficient of friction

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SUMMARY

The discussion focuses on calculating the minimum coefficient of friction required to prevent a farmer from slipping while using a pulley system. Key equations include F = m . a, Ffriction = μs . N, and the relationship between tension (T), normal force (N), and gravitational force (mg). The solution involves creating a free body diagram to balance vertical and horizontal forces, leading to the equation N = mg - Tsin(θ). This approach provides a clear method for determining the necessary frictional force.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with static friction and its coefficient (μs)
  • Ability to create and interpret free body diagrams
  • Knowledge of trigonometric functions in physics contexts
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  • Study the principles of free body diagrams in mechanics
  • Learn about static friction and its calculation methods
  • Explore tension in pulley systems and its effects on forces
  • Review Newton's laws of motion and their applications in real-world scenarios
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of force analysis in pulley systems.

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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