Question

A block lies on a plane raised an angle theta from the horizontal. Threeforces 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. Thecoefficient of friction is large enough to prevent the block fromsliding .Part A)Because the block is not moving, the sum ofthe y components of the forces acting on the block must bezero. Find an expression for the sum of the y componentsof the forces acting on the block, using coordinate system b.Express your answer in terms of someor all of the variables F_n, F_f, F_w, and theta.\sum f_y=Part B)Because the block is not moving, the sum ofthe x components of the forces acting on the block must bezero. Find an expression for the sum of the x componentsof the forces acting on the block, using coordinate system b.Express your answer in terms of someor all of the variables F_n, F_f, F_w, and theta.\sum F_{x}=0Part 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 youfound in the two previous parts, find an expression for F_n involving F_w and theta but not F_f.F_n =Diagram:In the diagram, a block is placed on an inclined surface with its both x and y components

Answer 1

A) N = W cos θ , B) fr = W sin θ, C) N = W cos θ

Step-by-step explanation:

To find the required expressions, let's make a free body diagram of the block, see attached.

In the problem of inclined plane the reference system used the x axis is parallel to the plane and the y axis is perpendicular

In this reference system the only force that we must decompose is the body weight F_w = W) for this we use trigonometry

Note that the angle of the plane is equal to the angle between the axis and the weight, therefore

sin θ =
`W_(x)` / W

cos θ =
`W_(y)` / W

`W_(x)` = W sin θ

`W_(y)` = W cos θ

B) Let us write Newton's second law for each axis, in this case as the block is still the acceleration is zero

X axis

fr -
`W_(x)` = 0

fr = W sin θ

A) Y Axis

N -
`W_(y)` = 0

N = W cos θ

C) N = W cos θ