Answer:
x = 4,138 m
Explanation:
For this exercise, let's use the rotational equilibrium equation.
Let's fix our frame of reference on the left side of the pivot, the positive direction for anti-clockwise rotation
∑ τ = 0
n₁ 0 - W L / 2 + n₂ 4 - W_woman x = 0
x = (- W L / 2 + 4n2) / W_woman
Let's reduce the magnitudes to the SI System
M = 6 lbs (1 kg / 2.2 lb) = 2.72 kg
M_woman = 130 lbs = 59.09 kg
Let's write the transnational equilibrium equation
n₁ + n₂ - W - W_woman = 0
n₁ + n₂ = W + W_woman
n₁ + n₂ = (2.72 + 59.09) 9.8
At the point where the system begins to rotate, pivot 1 has no force on it, so its relation must be zero (n₁ = 0)
n₂ = 605,738 N
Let's calculate
x = (-2.72 9.8 6/2 + 4 605.738) / 59.09 9.8
x = 4,138 m
F = 130 revs/min = 130/60 revs/s = 13/6 revs/s
t = 31s
wi = 2πf = 2π × 13/6 = 13π/3 rads/s
wf = 0 rads/s = wi + at
a = -wi/t = -13π/3 × 1/31 = -13π/93 rads/s²
wf² - wi² = 2a∅
-169π²/9 rads²/s² = 2 × -13π/93 rads/s² × ∅
∅ = 1209π/18 rads
n = ∅/2π = (1209π/18)/(2π) = 1209/36 ≈ 33.5833 revolutions.
Answer:
I think it is 5.6. This is my answer
