Mechanics - Pulley system finding coefficient of friction

[Roaku]

Homework Statement

Homework Equations

I believe:
F = m . a
F_friction = μ_s . N
F_friction = μ_s . 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 F_l = (70x9.81)cos(40) = 526N But there is now a variable F_friction 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.

 

[Infinitum]

Hi Roaku! Welcome to PF

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.

 

[azizlwl]

Homework Statement

View attachment 48197

Homework Equations

I believe:
F = m . a
F_friction = μ_s . N General Equatiom
F_friction = μ_s . 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 F_l = (70x9.81)cos(40) = 526N But there is now a variable F_friction 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.

 

[ehild]

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

 

[Infinitum]

Whoops, I mis-posted the equation.

Tsin\theta - mg + N = 0

Thanks for observing that, ehild