senseigmg

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This problem has been driving me nuts for 2 days.
A brrick with a density of 1.4x10^3 kg/m^3 is placed on top of a piece of styrofoam floating on water. If one half the volume of the styrofoam sinks below the water, what is the ratio of the volume of the styrofoam compared to the volume of the brick? (assume the styrofoam is massless.)
A. 0.7
B. 1.4
C. 2.8
D 5.6

Any help?
 

DHMO

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senseigmg said:
This problem has been driving me nuts for 2 days.
A brrick with a density of 1.4x10^3 kg/m^3 is placed on top of a piece of styrofoam floating on water. If one half the volume of the styrofoam sinks below the water, what is the ratio of the volume of the styrofoam compared to the volume of the brick? (assume the styrofoam is massless.)
A. 0.7
B. 1.4
C. 2.8
D 5.6

Any help?
An object will keep sinking until it displaces a volume of water with an equal mass. In this case, I think it's easiest to assume a volume/mass of the brick, then figure out the mass of the styrofoam. So, let's assume a volume of 1 m^3 for the brick, this will give the brick a mass of 1400 kg. Therefore, we need to displace a volume of water with a mass of 1400 kg. Knowing that water has a density of 1g/cm^3 (or 1000kg/m^3) tells us that we need to displace 1.4 m^3 of water with HALF of the styrofoam block. So the total volume of the styrofoam must be 2.8 m^3. Now, take the ratio of the styrofoam volume to the brick volume. 2.8m^3/1m^3 = 2.8--answer choice c.
 
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senseigmg

IR Fellow 2019-2020
10+ Year Member
Mar 9, 2005
78
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NYC Metro
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Resident [Any Field]
DHMO said:
An object will keep sinking until it displaces a volume of water with an equal mass. In this case, I think it's easiest to assume a volume/mass of the brick, then figure out the mass of the styrofoam. So, let's assume a volume of 1 m^3 for the brick, this will give the brick a mass of 1400 kg. Therefore, we need to displace a volume of water with a mass of 1400 kg. Knowing that water has a density of 1g/cm^3 (or 1000kg/m^3) tells us that we need to displace 1.4 m^3 of water with HALF of the styrofoam block. So the total volume of the styrofoam must be 2.8 m^3. Now, take the ratio of the styrofoam volume to the brick volume. 2.8m^3/1m^3 = 2.8--answer choice c.
OH MY GOD,
"...need to displace 1.4 m^3 of water with HALF of the styrofoam block." That finally made sense. So much more than the EK answer. Thanks a lot.