Question

A Styrofoam slab has thickness h and density ρs. When a swimmer of mass m is resting on it, the slab floats in fresh water with its top at the same level as the water surface. Find the area of the slab.

I assume the force exerted by the water needs to be equal to the force exerted by gravity on the object?

so I have
where
m is the mas of the swimmer
M is the mass of the Styrofoam

(M + m)g = B
since
M = ρA

we have that

(ρA + m)g = B
then
(ρA + m) = B/g
=
A = (B/g - m)/ρ

I'm pretty sure I'm wrong anyone able to help?

Answer 1

I mean I cant use this method to solve this because I dont know what B is

Answer 2

so I can just use

A = ((m+ M)g/g - m)/ρ
A = (M)/p

Answer 3

probably wrong

Answer 4

Well, this part is obviously right: (M + m)g = B

I'm still thinking about the rest

Answer 5

Maybe I'm still sleepy but how did you figure that M = pA

Answer 6

that is just a general formula

Answer 7

density = mass/volume

densityV = mass

V = A

Answer 8

Nm....I was thinking pressure not density. Yep, got it.

Answer 9

I really don't see anything wrong here

Answer 10

yeah but I assume the height comes into it

Answer 11

I think you're right...I need paper. One min

Answer 12

thanks I appreciate the help

Answer 13

No help just yet :P

Answer 14

I think I have it...it will take a minute to write this out though.

Answer 15

k thanks

Answer 16

Starting:\[(M+m)g=B\]\[M+m=\frac{B}{g}\]\[ M=\rho V=\rho Ah\]\[\rho Ah+m=\frac{B}{g}\]\[\rho Ah=\frac{B}{g}-m\]\[A=\frac{\frac{B}{g}-m}{\rho h}\]Check it but I think that's correct.

Answer 17

I used the normal density formula...not surface density.

Answer 18

give me a second getting error

Answer 19

why is pV = pAh ?

Answer 20

That's where the mistake was made...I'm aggravated at myself for not seeing it immediately.

V = area x height

Answer 21

oh true

Answer 22

You had it right initially...except for that part.

Answer 23

thanks :)

Answer 24

you're welcome :)