Octane (C8H18) is burned with dry air. The volumetric analysis of the products on a dry basis is as below. (Fig. 15–12) Determin
e (a) the air–fuel ratio, (b) the percentage of theoretical air used, and (c) the amount of H2O that condenses as the products are cooled to 25°C at 100 kPa
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Answer:
w = w₀ M / (M + 2m)
Explanation:
This exercise can be solved using the concepts of conservation of angular momentum
L = I w
Let's write in angular momentum in two points
Initial. Before impact
L₀ = I w₀
Final. After the rock has stuck
= I w + (m r²) w
The system is formed by the disk and the rock, so that the forces and moments during the crash are internal and the angular momentum is preserved
L₀ =
I w₀ = (I + m r²) w
w = w₀ I / (I + m r²)
The roundabout is a disk so its moment of inertia is
I = ½ M r²
w = w₀ ½ Mr² / (½ M r² + mr²)
w = w₀ ½ M / (½ M + m)
w = w₀ ½ M2 / (M + 2m)
w = w₀ M / (M + 2m)