Physics Help.....?

Question

A polar bear partially supports herself by pulling part of her body out of the water onto a rectangular slab of ice. The ice (with specific gravity of 0.917) sinks down so that only half of what was once exposed now is exposed, and the bear has 70% of her volume and weight out of the water. Estimate the bear's mass, assuming that the total volume of ice is 10 m^3, and the bear's specific gravity is 1.0.
Answer is 7.9 x 10^2 kg
Can someone please show the solution for this problem...

Answer 1

First let's compute the volume of ice above water
dV=(r_water-r_ice)V
dV- volume of ice above water
r_water - specific gravity of water (1.0)
r_ice - specific gravity of water (.0917)
V- total volume of ice

Now since half of what was above the water dipped down then the 70% of beard mass is responsible for it. Also bear in mind( no pun intended) that bears density is the same as that of water so there is no effective buoyancy force exerted on the bears body in the water. With that in mind
Mass of the bear above the water = volume of ice dipped times specific gravity of water less that of ice. We have

.7M=.5 dV(1-.0.917)

So M= .5 dV(1-.0.917)/.7=
M=.5 (r_water-r_ice)V (1-.0.917)/.7=
M=(.5/.7) (1-.0.917)^2 (10 m^3)=
M=(0.71) (0.006889) (10)= 0.0489119
M=0.049 (what?)

Since we are dealing with specific gravity it is a ratio of density of a particular substance to water. So we need a proportionality constant to get us on the right track. Since density of water is 1000kg/m^3 our proportionality constant is 1000.

The bear m=kM= 1000x0.049=49kg. it must be a very small cub or my computations are off.

Okay let’s work the problem in reverse

m=790kg (sounds about right)
m1=.7m=553kg (this is mass of the bear above the water)
Now let’s compute amount of ice required to keep her afloat.
V=m1/dr
dr – is the difference in densities (1000kg/m^3 – 917kg/m^3)= 83kg/m^3
then
V=553/83=6.66 m^3 Wow! The 70 % of the bear should have displaced 6.7 cubic meters of water by sinking the ice of that volume. But we had only 10m^3 to begin with? So it is either the problem statement is wrong or the answer is wrong.