Problem: 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 .

FREE Expert Solution

(A) 

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

The y-component is equal to Frsinθ directed in the positive y-axis.

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

The y-component is equal to Fncosθ directed in the positive y-axis.

Fw is directed in the negative y-axis.

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Problem Details

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

MFS_1l_1.jpg

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,F_n_vec, using vertical coordinate system b. In these coordinates you will find the magnitude F_n appearing in both the x and 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 F_n, F_f, F_w, and theta.

(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 F_n, F_f, F_w, and theta.

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

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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 Inclines with Friction concept. You can view video lessons to learn Inclines with Friction. Or if you need more Inclines with Friction practice, you can also practice Inclines with Friction practice problems.