Question

station #3: friction on incline (5 min)
problem: 3.0 kg block on 30° incline with μₛ = 0.50.
quick calculations:
f1 = f₉ sin θ = ______
fₙ = f₉ cos θ = ______
fᵢ(max) = μₛ fₙ = ______
is the block in equilibrium? ______ (show: does fᵢ≥ f1?)
prepare to teach the class: how to resolve forces on an incline.

Explanation:

Step1: Calculate \(F_1 = F_g \sin\theta\)

\(F_g = mg = 3.0\,\text{kg} \times 9.8\,\text{m/s}^2 = 29.4\,\text{N}\); \(F_1 = 29.4\sin30^\circ = 29.4 \times 0.5 = 14.7\,\text{N}\)

Step2: Calculate \(F_N = F_g \cos\theta\)

\(F_N = 29.4\cos30^\circ = 29.4 \times \frac{\sqrt{3}}{2} \approx 25.46\,\text{N}\)

Step3: Calculate \(F_f(\text{max}) = \mu_s F_N\)

\(F_f(\text{max}) = 0.50 \times 25.46 \approx 12.73\,\text{N}\)

Step4: Check equilibrium (Is \(F_f \geq F_1\)?)

\(12.73\,\text{N} < 14.7\,\text{N}\), so no.

Answer:

14.7 N
≈25.46 N
≈12.73 N
No