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EK Study Guide Lecture 2 #51 (pg.73)
#1 Posted : Tuesday, June 02, 2020 11:18:22 PM
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I don’t understand how they even began to solve this problem. I originally attempted to find the density of the block and of the brick then convert it to volume but because the styrofoam has no mass I couldn't solve it that way. Could you explain how to properly solve this? I looked at the solution and it made no sense to me.
#2 Posted : Thursday, June 04, 2020 10:01:58 PM
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Hello! This is definitely a tricky question.

Recall that for a floating object, the mass of water displaced = mass of brick+styrofoam (in this case mass of styrofoam is 0). So m_water = m_brick. Also recall that density, rho=m/v or m = rho x v. if m_water = m_brick then rho_water x v_water = rho_brick x v_brick. we know that rho_brick/rho_water = 1.4. If we rearrage our previous formula, rho_brick/rho_water= v_water/v_brick = 1.4. We also know that the volume of water dispaced = 1/2 styrofoam volume, so v_water = 1/2 v_styro.

so: v_water = 1/2v_styro = 1.4v_brick. (1.4~3/2) —> to rearrange this: v_styro ~ (3/2)*(2)v_brick ~ 3v_brick giving you the answer C.
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