A small box is held in place against a rough vertical wall bysomeone pushing on it with a force directed upward at 28 degreesabove horizontal. The coeffients of static and kineticfriction between the box and the wall are 0.40 and 0.30, respectively. The box slides down unless the applied forcehas a magnitude 23N. What is the mass of the box?

m = 1.9287 Kg

Explanation:

Given

∅ = 28º

μs = 0.40

μk = 0.30

F = 23 N

m = ?

We can apply

∑Fh = 0 (+→)

N - Fh = 0 ⇒ N = Fh = F*Cos ∅

then N = F*Cos ∅

∑Fv = 0 (+↑)

⇒ Fy - W + Ff = 0

where

Fy = F*Sin ∅

W = m*g

Ff = μs*N = μs*F*Cos ∅

then

⇒ Fy - W + Ff = F*Sin ∅ - m*g + μs*F*Cos ∅ = 0

⇒ m = (F / g) * (Sin ∅ + μs*Cos ∅)

⇒ m = (23 N / 9.81 m/s²) * (Sin 28º + 0.40*Cos 28º)

⇒ m = 1.9287 Kg