Answer to Question #241362 in Mechanics | Relativity for Anas

Question

Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coef-

ficient of static friction between the block and ramp is 0.350, what maximum angle can

the ramp make with the horizontal before the block starts to slip down?

Answer 1

F =$2.50 \times9.8$ = 24.5N

Fp =$24.5\times sinA =$ Force parallel with plane.

Fv =$24.5\times cosA$ = Force perpendicular to

plane.

uFv$= 0.35F_v =$ Force of friction.

Fp - 0.35Fv = ma,

a = 0(block at rest),

Fp -0.35Fv = 0,

Fp = 0.35Fv,

$24.5\times sinA = 0.35\times 24.5\times cosA,$

Divide both sides by 24.5:

sinA = $0.35\times cosA$

Divide both sides by cosA:

$sinA / cosA$ = 0.35,

$sinA / cosA$ = TanA,

TanA = 0.35,

maximum angle is

$A = 19.3\degree$