Finding the force up an incline given horizontal force

AI Thread Summary
To find the force up an incline given a horizontal force, it's essential to understand the relationship between the applied force and the incline's angle. The correct approach is to use the formula Fx = Fapp * cos(θ), where Fx is the component of the applied force acting up the slope. The confusion arises from misinterpreting the triangle drawn for the forces; the hypotenuse should represent the total applied force, while the adjacent side corresponds to the force component acting along the incline. The discussion clarifies that the horizontal force acts as a headwind affecting the skier's motion down the slope. Understanding these components is crucial for solving the problem accurately.
OneObstacle
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Homework Statement


I need help with part of a problem. I am having problems understanding just how to find the force up an incline when a horizontal force ("headwind") is given.


Homework Equations





The Attempt at a Solution


When drawing a triangle to figure it out I draw the hypotenuse as x (force I need to find) and the side adjacent to angle θ as Fapplied. From this, I get cosθ = Fapp/x, therefore x=Fapp/cosθ. However, my online homework listed it as Fapp*cosθ. Did I draw the triangle wrong?
 
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Welcome to PF!

Hi OneObstacle! Welcome to PF! :smile:
OneObstacle said:
… how to find the force up an incline when a horizontal force ("headwind") is given.
…
When drawing a triangle to figure it out I draw the hypotenuse as x (force I need to find) and the side adjacent to angle θ as Fapplied. From this, I get cosθ = Fapp/x, therefore x=Fapp/cosθ. However, my online homework listed it as Fapp*cosθ. Did I draw the triangle wrong?

I don't understand which of x and Fapp is the force to be applied, and which is the wind. :confused:

(I also don't understand how you can have a horizontal headwind if you're facing up an incline. :redface:)
 
The original problem is a skier heading down an incline (sorry, confusing wording). Fapp is the headwind heading into the slope, and Force x is what I randomly assigned the force of the wind acting on the skier.
 
Hi OneObstacle! :smile:

(just got up :zzz:)
OneObstacle said:
The original problem is a skier heading down an incline (sorry, confusing wording). Fapp is the headwind heading into the slope, and Force x is what I randomly assigned the force of the wind acting on the skier.

ohh! … you mean Fx is the component of the wind force in the x direction (ie up the slope)?

ok, then your book is correct …

don't start drawing triangles, just use this rule:

to find the component of a (complete) force, we always multiply by cos of the angle between

Fx = Fappcosθ :smile:​
 

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