Question

A block weighing 87.5 N rests on a plane inclined at 25.0° to
the horizontal. A force *F* is applied to the object at
50.0° to the horizontal, pushing it upward on the plane. The
coefficients of static and kinetic friction between the block and
the plane are, respectively, 0.377 and 0.156.

(a) What is the minimum value of *F* that will prevent
the block from slipping down the plane?

N

(b) What is the minimum value of *F* that will start the
block moving up the plane?

N

(c) What value of *F* will move the block up the plane with
constant velocity?

N

Answer #1

here,

weight , W = 87.5 N

theta = 25 degree

phi = 50 degree

a)

the minimum value of F that will prevent the block from slipping down the plane be F

F * cos(phi) + us * ( m * g * cos(theta) - F * sin(theta) ) = m * g * sin(theta)

F * cos(50) + 0.277 * ( 87.5 * cos(25) - F * sin(50)) = 87.5 * sin(25)

solving for F

F = 34.9 N

b)

the minimum value of F that will prevent the block from moving up the plane be F

F * cos(phi) = us * ( m * g * cos(theta) - F * sin(theta) ) + m * g * sin(theta)

F * cos(50) = 0.377 * ( 87.5 * cos(25) - F * sin(50)) + 87.5 * sin(25)

solving for F

F = 71.8 N

c)

let the minimum force be F

F * cos(phi) = uk * ( m * g * cos(theta) - F * sin(theta) ) + m * g * sin(theta)

F * cos(50) = 0.156 * ( 87.5 * cos(25) - F * sin(50)) + 87.5 * sin(25)

solving for F

F = 64.7 N

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