Question

An object made of an unknown material is placed on a surface of another unknown material. You only have the maximum value of static friction for the masses below.

Max force of static friction (N)	Mass of Unknown Material (Kg)
17	4
29	9
71	18
106	26
214	58
364	90
455	112

With one of the masses, you begin to raise the surface, increasing the angle of the incline slowly. When it is on the verge of slipping, what angle do you expect it to be at?

Answer 1

verge of slipping means the downward component of weight is exactly equal to maximum force of static friction (F)

then

F = mgsin

select any mass from the given table and corresponding maximum value of static friction.

I will select m = 9 kg, then F = 29 N

29 = 9 * 9.8 * sin

29 = 88.2 * sin

sin = 29 / 88.2

sin = 0.3287

= arcsin (0.3287)

= 19.19 degree

_____________________-

Let's do for another mass

select m = 90 kg , then F = 364 N

so,

364 = 90 * 9.8 * sin

= 24.37 degree