**(A)**

For the friction force, θ is measured from the x-axis.

The y-component is equal to F_{r}sinθ directed in the positive y-axis.

For the normal force, θ is measured from the y-axis.

The y-component is equal to F_{n}cosθ directed in the positive y-axis.

F_{w} is directed in the negative y-axis.

A block lies on a plane raised an angle from the horizontal. Three forces act upon the block:, the force of gravity; , the normal force; and , the force of friction. The coefficient of friction is large enough to prevent the block from sliding (Intro 1 figure).

Now you are going to ignore the general rule (actually, a strong suggestion) that you should pick the coordinate system with the most vectors, especially unknown ones, along the coordinate axes. You will find the normal force,, using vertical coordinate system b. In these coordinates you will find the magnitude appearing in both the *x* and *y *equations, each multiplied by a trigonometric function.

(A) Because the block is not moving, the sum of the *y* components of the forces acting on the block must be zero. Find an expression for the sum of the *y* components of the forces acting on the block, using coordinate system b.

Express your answer in terms of some or all of the variables , , , and .

(B) Because the block is not moving, the sum of the *x* components of the forces acting on the block must be zero. Find an expression for the sum of the *x* components of the forces acting on the block, using coordinate system b.

Express your answer in terms of some or all of the variables , , , and .

(C) To find the magnitude of the normal force, you must express in terms of since is an unknown. Using the equations you found in the two previous parts, find an expression for involving and but not .

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Inclined Planes with Friction concept. You can view video lessons to learn Inclined Planes with Friction. Or if you need more Inclined Planes with Friction practice, you can also practice Inclined Planes with Friction practice problems.

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Based on our data, we think this problem is relevant for Professor Yost's class at OKSTATE.