For a new TV series "Stupidity Factor contestants are dropped into the ocean (p 1030 kg/ms) along with a Styrofoam soo kg/ms block that is mm x 3 mm X 20 cm thick. If too many contestants climb aboard the block and it sinks below the water surface, they are declared "stupid" and abandoned at sea. Find the maximum number of 7o kg contestants that the block can hold. (No fractional contestants, please. They hate it when that happens.

For a new TV series "Stupidity Factor contestants are dropped into the ocean (p=1030 kg/m³) along with a Styrofoam p=3oo kg/m³ block that is 2m x 3 m X 20 cm thick. If too many contestants climb aboard the block and it sinks below the water surface, they are declared "stupid" and abandoned at sea. Find the maximum number of 7o kg contestants that the block can hold. (No fractional contestants, please. They hate it when that happens.

answer:

volume of styrofoam block=V=2m x 3m x 0.20m =1.2m³

density of styrofoam=ρs=300kg/m³

mass of styrofoam=ms=v(ρs)=1.2 x 300=360kg

weight of styrofoam = ws=(ms)g=360 x 9.8=3528N

consider number of contestants= n

toatal weight of ccontestants=W=n(70 x 9.8)=n(686N)

since, styrofoam fully submerged into water, then bat force,

B=ρ(vs)g=1030 x 1.2 x 9.8 = 12112.8N

At equilibrium,

B - W - Ws = 0

12112.8 - 686n - 3528 = 0

[tex]n=\frac{12112.8-3528}{686}=12.5[/tex]

n=12 person(contestants)