Finding the direction of the force knowing the mu static

In summary: If you do know, just find the derivative, set it equal to 0, and solve for Θ. (Hint: I'm pretty sure the maximum will be at 0°.)In summary, to start the crate moving with the least possible applied force, the force should be applied horizontally, at an angle of 0 degrees above the horizontal. This is found by setting the equation Fcosθ = µs . (W - Fsenθ) in the form F * f(θ) = constant and maximizing the function f(θ). The maximum value of f(θ) is at 0 degrees, which corresponds to a horizontal force.
  • #1
Mafalda
1
0
1. A crate resting on a rough horizontal floor is to be moved horizontally. The coefficient of static friction is 0.40. To start the crate moving with the least possible applied force, in what direction should the force be applied?

a. Horizontal

b. 24 degrees below horizontal

c. 22 degrees above the horizontal

d. 24 degrees above the horizontal

e. 66 degrees below the horizontal

Almost 1 hour on this and I really cannot find how to do it! This is the work I’ve done

Fx-fs = 0 <=> Fcosθ = µs . N

Fsenθ + N - W = 0 <=> N = W - Fsenθ

So:
Fcosθ = µs . (W - Fsenθ)

And then I can’t continue! I really need to understand! Thanks!
 
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  • #2
Mafalda said:
1. A crate resting on a rough horizontal floor is to be moved horizontally. The coefficient of static friction is 0.40. To start the crate moving with the least possible applied force, in what direction should the force be applied?

a. Horizontal

b. 24 degrees below horizontal

c. 22 degrees above the horizontal

d. 24 degrees above the horizontal

e. 66 degrees below the horizontal

Almost 1 hour on this and I really cannot find how to do it! This is the work I’ve done

Fx-fs = 0 <=> Fcosθ = µs . N

Fsenθ + N - W = 0 <=> N = W - Fsenθ

So:
Fcosθ = µs . (W - Fsenθ)

And then I can’t continue! I really need to understand! Thanks!
Welcome to the PF. :smile:

I think I know the answer, but I'd like to see your Free Body Diagram (FBD). Could you please Upload a JPEG or PDF of your FBD for this problem, and show how you did the math to minimize the total force vecror needed? Thanks.
 
  • #3
It will help to gather all the terms containing F and ##\theta## in one side of the equation. Then you ll have the equation in the form

##F\cdot f(\theta)=...## where ##f(\theta)## is a function of theta containing sine and cosine of theta.. In order to minimize F, maximize ##f(\theta)##. It will not be too hard to find the value of theta where f is at maximum.
 
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  • #4
As @Delta² stated, get F on one side, then if you have F multiplied by a function of Θ equal to some constant, you can maximize the function. You can try plotting it vs Θ if you don't know how to find the maximum.
 
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Related to Finding the direction of the force knowing the mu static

1. What is the definition of "mu static" in relation to finding the direction of force?

"Mu static" refers to the coefficient of static friction, which is a measure of how difficult it is for two surfaces to slide against each other without any movement occurring.

2. How does knowing the value of mu static help in determining the direction of force?

Knowing the value of mu static allows us to calculate the maximum amount of force that can be applied before the object will start to slide. This helps us determine the direction of force, as we know that the applied force must be less than the maximum static friction force in order for the object to remain stationary.

3. Can the direction of force be determined without knowing the value of mu static?

Yes, the direction of force can be determined based on the relative magnitudes and directions of all the other forces acting on the object. However, knowing the value of mu static can provide a more precise calculation.

4. How is the direction of force affected by changes in the value of mu static?

If the value of mu static increases, the maximum static friction force also increases. This means that a greater force can be applied before the object starts to slide, potentially changing the direction of force. Conversely, if the value of mu static decreases, the maximum static friction force decreases and the direction of force may also change.

5. Are there any other factors besides mu static that affect the direction of force?

Yes, there are other factors that can affect the direction of force, such as the angle of the surface, the weight and mass of the object, and the presence of any other external forces. These should all be taken into consideration when determining the direction of force.

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