Box resting on an inclined plane

AI Thread Summary
To determine the smallest force applied perpendicular to a box resting on a 45-degree inclined plane, the static friction and gravitational forces must be balanced. The normal force (Fn) is calculated using the equation Fn = Fgx/mu static, where Fgx represents the gravitational force component along the ramp and mu static is the coefficient of static friction. This relationship arises because static friction (Fs) equals the product of the coefficient of static friction and the normal force, which must counteract the gravitational component to keep the box at rest. The discussion highlights the importance of understanding the balance of forces and the role of static friction in maintaining equilibrium on an incline. Accurate calculations are essential for determining the required applied force to prevent the box from sliding.
JamesW
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Homework Statement



A box with a mass of 22kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of static friction is 0.78

determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp if the box is to remain at rest?

Homework Equations



F=ma

The Attempt at a Solution



F f (static friction) + Fgx = 0

F n = Fgy + F a

Fa = F n - Fgy

I have viewed a thread and to calculate F n (normal force) they divided Fgx/mu static. I was wondering why this was?
 
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WHY IS Fn = Fgx/ mu static ?
 
because Fs=(mu static)(Fn)
 
which is valid if friction _exactly_ cancels "g sin theta" ...
 

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