coeffcient of friction please helpe???????????

Question

The coefficient of friction between a box and an inclined plane is 0.35. What is the maximum angle required for the box to stay on the incline and not slide of the incline? if the weight of the object is 100N

some one told me :
100*sin x =0.35*100*cos x
sin x/cos x = 0.35
tan x = 0.35
x = Arctan(0.35)
x = 19.29 degrees

do i need to put the 19.25 in to the formula. like:
100sin19.25 gives me 33.2 degrees, is 33.2 the the maximum angle that the box can stay on the incline plane

please help

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Answer 1

no, the 19.29 is the angle. The arctan function returns the angle.

so if tan(x) = 0.5, then Arctan(0.5) = x

The weight of the box actually isn't relevant to the problem

make sense?

Answer 2

I'm guessing that you mean that the downward force of the object is 100 Newtons. In a one standard Earth gravity (9.8 M/s/s) that would mean the object has a mass of

100N/9.8M/s/s = 10.204 Kg (derived from f = ma)

Now, as the plane is tilted 'upwards' the force exerted by gravity can be broken down into two vector components. The first one (usually called the 'normal' force) is at right angles to the inclined plane and the 2'nd one (usually called the 'parallel' force) is parallel to the inclined plane.

The normal force is given by

Fn = 100*cos(x)

where x is the angle (measured from horizontal) of the plane. The parallel force is given by

Fp = 100*sin(x)

The object will begin to slide when

Fp > .35*Fn

but, more commonly, we say that the object begins to slide when the angle, x, is greater than that found at

Fp = .35*Fn

making the substitutions

100*sin(x)/100*cos(x) = .35

and

tan(x) = .35

so that

x = arctan(.35) = 19.29 degrees

The object will begin to slide when the angle of the inclined plane exceeds 19.29 degrees.

Note also that the object will accelerate since, once it begins moving, the coefficient of friction changes from the 'static' value to the 'dynamic' value (which is always lower) As a result, there will be a net force on the object and, since f=ma, the object will accelerate.


Doug

Answer 3

no just 19.29 is the anwser as it is called angle of repose..u don't have to put it back again in some equation

Answer 4

I make it arctan 0.35=21.4 degrees.