A mass of a liquid of density p is thoroughly mixed with an equal mass of another liquid of density 2p. No change of the total volume occurs. What is the density of the liquid mixture?
The answer is 4p\3 but I have absolutely no idea how to get there. Pretty disappointed at myself right now.
The answer is 4p\3 but I have absolutely no idea how to get there. Pretty disappointed at myself right now.
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no need to be dissapointed - your problems I have noted require you to think out of the box
We can pick any one mass and scale up.
density p means mass p/unit volume so let's pick mass p
first liquid volume = 1
second liquid is also mass p so its volume is 1/2
total volume = 3/2
total mass = 2p
2p/(3/2) = 4p/3 as predicted
We can pick any one mass and scale up.
density p means mass p/unit volume so let's pick mass p
first liquid volume = 1
second liquid is also mass p so its volume is 1/2
total volume = 3/2
total mass = 2p
2p/(3/2) = 4p/3 as predicted
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Mass is density x volume.
Volume = mass / density
Volume of first is m/ρ
volume of second is m/2ρ
total volume is the sum, (m/ρ)(1 + 1/2) = (m/ρ)(3/2) = 3m/2ρ
total mass is m+m = 2m
overall density = M/V = 2m / (3m/2ρ) = 2m2ρ / 3m = 4ρ/3
Volume = mass / density
Volume of first is m/ρ
volume of second is m/2ρ
total volume is the sum, (m/ρ)(1 + 1/2) = (m/ρ)(3/2) = 3m/2ρ
total mass is m+m = 2m
overall density = M/V = 2m / (3m/2ρ) = 2m2ρ / 3m = 4ρ/3