Calculating Buoyant Force of Ice to Find Mass - No Hints

[cscott]

70% of a mass is supported by a slab of ice and the ice sinks down so that only half of what was previously exposed now is exposed. What is the mass assuming that the ice has a volume of 10 m^3 and the mass has a specific gravity of 1.0?

Why can't I use the buoyant force of the ice before and after the extra weight is added and subtract to get the weight of the object itself? I get 539.5 kg while the textbook says 790 kg. Only hints please!

 

[Doc Al]

Why can't I use the buoyant force of the ice before and after the extra weight is added and subtract to get the weight of the object itself?

Sounds good to me. Show what you did exactly.

 

[cscott]

Alright, well since $F_B = w$ when an object is floating, the buoyant force is $F_B = \rho_{ice} Vg = (0.917 \times 10^3)(10)(9.8) = 9.0 \times 10^4N$.

$$\frac{0.917 \times 10^3}{1.00 \times 10^3} + \frac{1}{2}(1 - 0.917) = 0.9585$$
for the fraction of the ice submerged once the unkown mass is put on.

With this, the buoyant force is $F_b = (1.00 \times 10^3)(0.9585 \cdot 10)(9.8) = 9.4 \times 10^4N$

$$W_{object} = 9.4 \times 10^4 - 9.0 \times 10^4 = 4.0 \times 10^3N$$

$$\frac{4.0 \times 10^4 \cdot 1.3}{9.8} = 530 kg$$

I rounded the numbers this time.

 

[Doc Al]

Your method looks OK to me (assuming we are interpreting the problem correctly--why do they specify the specific gravity of the mass?) but I would divide by 0.7 instead of multiply by 1.3.

 

[cscott]

Your method looks OK to me (assuming we are interpreting the problem correctly--why do they specify the specific gravity of the mass?) but I would divide by 0.7 instead of multiply by 1.3.

The fact that they gave the specific gravity had me starting to work with volume but I could never get any sensible answers. If it makes any difference, this is how the question is worded in the book:

A polar bear paritally supports herself by pulling part of her body out of the water onto a rectangular slab of ice. The ice sinks down so that only half of what was once exposed now is exposed, and the bear has 70 percent of her volume (and weight) out of the water. Estimate the bear's mass, assuming that the total volume of the ice is 10 m^3, and the bear's specific gravity is 1.0.

 

[Doc Al]

Since the specific gravity is one, it makes no difference--the buoyant force on the bear equals the weight of her submerged portion. (Were it something else, it would matter.)

 

[cscott]

Ah, ok. I guess the textbook answer is just wrong...?

Thanks for your help BTW.

 

[Doc Al]

I guess the textbook answer is just wrong...?

Yep, seems wrong to me.