Force Applied to Box on Incline

AI Thread Summary
To determine the normal force acting on a box on an incline, start by analyzing the forces involved, including the applied force and friction. Since the box is initially at rest, the static friction coefficient should be used to assess whether the applied force overcomes static friction. The applied force's direction must be clarified, as it affects the net force calculations. If the applied force is greater than the maximum static friction force, the box will move, necessitating a switch to the kinetic friction coefficient. Ultimately, calculating the normal force involves considering the weight of the box, the angle of the incline, and the applied force.
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A force is applied to a box that is initially at rest on an inclined surface. The incline is at an angle θ=20.0° above horizontal. The mass is m=36kg and the vertical force is Fapp= 48N. Between the box and the inclined surface the coefficient of static friction, μs=.240 and a coefficient of kinetic friction, μk=.150. Use this information to fine the normal force in this situation.

I am confused on where to start. Do I have to use both friction coefficients?
 
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Is the applied force vertically up or vertically down? Either way, draw the free body diagram.
Which coefficient to use depends on whether things move. You know it is initially at rest, so try supposing it stays that way. Use the information provided to find whether static friction is overcome. If it is, switch to using the coefficient for kinetic friction.
 
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