Answer:
0.00016 kg
Explanation:
Given:
Power = P = 1.2 × 10⁹ Watts
Power = work done / Time
efficiency = 0.30
Input power = 1.2 × 10⁹ / 0.30 = 4 × 10⁹ W
Energy = 4 × 10⁹ x 60 x 60 = 1.44 x 10¹³ joules
E = m c² , where c is the speed of light and m is the mass.
⇒ mass = m = E / c² = (1.44 x 10¹³) / (3 × 10⁸ )²
= 0.00016 kg
From an energy balance, we can use this formula to solve for the angular speed of the chimney
ω^2 = 3g / h sin θ
Substituting the given values:
ω^2 = 3 (9.81) / 53.2 sin 34.1
ω^2 = 0.987 /s
The formula for radial acceleration is:
a = rω^2
So,
a = 53.2 (0.987) = 52.494 /s^2
The linear velocity is:
v^2 = ar
v^2 = 52.949 (53.2) = 2816.887
The tangential acceleration is:
a = r v^2
a = 53.2 (2816.887)
a = 149858.378 m/s^2
If the tangential acceleration is equal to g:
g = r^2 3g / sin θ
Solving for θ
θ = 67°
It takes 365 1/4 days for the Earth to complete 1 full revolution.
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