A water droplet evaporates before they reach the ground. Figure 1: Water droplets [source] In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at timet is r(t) = t+ ro- (Hint: m = pV,V =Tr³, S = 4nr?).
A water droplet evaporates before they reach the ground. Figure 1: Water droplets [source] In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at timet is r(t) = t+ ro- (Hint: m = pV,V =Tr³, S = 4nr?).
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![A water droplet evaporates before they reach the ground.
ond ord
Figure 1: Water droplets [source]
In this situation, a few assumptions are made:
a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical
while evaporating.
b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S.
There is no air-resistance and downward direction is the positive direction.
quat
To describe this problem, given that p is the mass density of water, rois the radius of water before it
drops, m is the water mass, V is the water volume andk is the constant of proportionality.
QUESTION:
(1) From assumption (b), show that the radius of the water droplet at time t is
or
r(t) = (=)t+ro-
%3D
(Hint: m = pV,V =tr³, S = 4nr²).
4
TTr
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fbbe91e-b101-441b-b5fc-9477065585b8%2Fad00fb47-66af-44dc-a81d-e969fa5e2d55%2Fovzw8z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A water droplet evaporates before they reach the ground.
ond ord
Figure 1: Water droplets [source]
In this situation, a few assumptions are made:
a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical
while evaporating.
b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S.
There is no air-resistance and downward direction is the positive direction.
quat
To describe this problem, given that p is the mass density of water, rois the radius of water before it
drops, m is the water mass, V is the water volume andk is the constant of proportionality.
QUESTION:
(1) From assumption (b), show that the radius of the water droplet at time t is
or
r(t) = (=)t+ro-
%3D
(Hint: m = pV,V =tr³, S = 4nr²).
4
TTr
3
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