Answer:
The total surface are of the bowl is given by: 0.0532*pi m² (approximately 0.166533 m²)
Explanation:
The total surface area of the semi-spherical bowl can be decomposed in three different sections: 1) an outer semi-sphere of radius 12 cm, 2) an inner semi-sphere of radius 10 cm, and 3) the edge, which is a 2-dimensional ring with internal radius of 10 cm and external radius of 12 cm. We will compute the areas independently and then sum them all.
a) Outer semi-sphere:
A1 = 2*pi*r² = 2*pi*(12 cm)² = 288*pi cm² = 904.78 cm²
b) Inner semi-sphere:
A2 = 2*pi*(10 cm)² = 200*pi cm² = 628.32 cm²
c) Edge (Ring):
A3 = pi*(r1² - r2²) = pi*((12 cm)²-(10 cm)²) = pi*(144-100) cm² = 44*pi cm² = 138.23 cm²
Therefore, the total surface area of the bowl is given by:
A = A1 + A2 + A3 = 288*pi cm² + 200*pi cm² + 44*pi cm² = 532*pi cm² (approximately 1665.33 cm²)
Changing units to m², as required in the problem, we get:
A = 532*pi cm² * (1 m² / 10, 000 cm²) = 0.0532*pi m² (approximately 0.166533 m²)
An incompressible flow field F in a 3D cartesian grid with components u,v,w:
F = u + v + w
where u,v,w are functions of x,y,z
Must satisfy:
∇·F = du/dx + dv/dy + dw/dz = 0
We have a field F defined:
F = u+v+w, u = ax+byz, v = cy+dxz
du/dx = a, dv/dy = c
Recall ∇·F = 0:
∇·F = du/dx + dv/dy + dw/dz = 0
a + c + dw/dz = 0
dw/dz = -a-c
Solve for w by separation of variables:
w = ∫(-a-c)dz
w = -az - cz + f(x,y)
f(x,y) is some undetermined function of x and y
The question states that w is not a function of x and y, therefore f(x,y) = 0...
w = -az - cz
Weight = (mass) x (acceleration of gravity)
Acceleration of gravity = 9.81 m/s² on Earth, 1.62 m/s² on the Moon.
The feather's weight is . . .
On Earth: (0.0001 kg) x (9.81 m/s²) = <em>0.000981 Newton </em>
On the Moon: (0.0001 kg) x (1.62 m/s²) = <em>0.000162 N</em>
The presence or absence of atmosphere makes no difference. In fact, the numbers would be the same if the feather were sealed in a jar, or spinning wildly in a tornado, or hanging by a thread, or floating in a bowl of water or chicken soup. Weight is just the force of gravity between the feather and the Earth. It's not affected by what's around the feather, or what's happening to it.
Answer:
0.24 ? I hope that was the answer you were looking for.
Explanation:
