Three applied forces F1= 20N, F2= 40N and F3= 10N act on a crate with a mass of 2kg on an incline with θ = 30o, φ = 60o and μk = 0.2, find the acceleration

Answer 1

Wc = m*g = 2kg * 9.8N/kg = 19.6 N. = Wt.
of crate.

Fc = 19.6N. @ 30 Deg. = Force of crate.
Fp = 19.6*sin30 = 9.8 N.=Force parallel
to incline.
Fv = 19.6*cos30 = 17.0 N. = Force
perpendicular to incline.

Fap = 20 + 40 + 10 = 70 N. = Force applied.

Fn = Fap - Fp - Fk
Fn = 70 - 9.8 - 0.2*17 = 6.4 N. = Net
force.

a = Fn/m = 6.4 / 2 = 3.2 m/s^2.

NOTE: It is assumed the 3 forces act
parallel to and up the plane.

Answer 2

Correction: Fn = 56.8 N.
a = 56.8 / 2 = 28.4 N.