Solving Flotation Problem: Estimate a Polar Bear's Mass

  • Thread starter WhackyWookie
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In summary, the polar bear is partially supported by a slab of ice with a specific gravity of 0.917. The ice sinks, and the bear has 70% of her weight and volume out of the water. The mass of the bear can be calculated using the equation for weight of an object in a submerged environment based on the weight of the ice, the bear's specific gravity, and the volume of the bear.
  • #1
WhackyWookie
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The problem is:

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.

I have tried to solve it using the equivalence of the ratios between the volume of displaced water and volume of object and density of object and density of fluid, but have been consistently getting wrong answers. Any help is appreciated.
 
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  • #2
WhackyWookie said:
The problem is:

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.

I have tried to solve it using the equivalence of the ratios between the volume of displaced water and volume of object and density of object and density of fluid, but have been consistently getting wrong answers. Any help is appreciated.
As a general approach, do it like this: You can find out what volume of ice is originally submerged (without the bear on it). Now, set up an equation where the net force is zero. The forces acting on the system would be the buoyant force on 30% of the bear, the buoyant force on the ice (and you should be able to figure out what volume of ice is in the water based on the previous calculation, and the fact that another 50% is submerged), the weight of the ice, and the weight of the bear. Solve for the weight of the bear, and thus determine the mass. Also, you can express the volume of the bear in terms of its specific gravity and its mass. So you'll have an "m" variable in two places, but still only one unknown and one equation, meaning you can still solve it.
 
  • #3
thnx for ur explanation, but the answer I got using ur method is the same as I got before (592.9 kg), which is inconsistent with the 790 kg answer listed on the back of the book.
 
  • #4
WhackyWookie said:
thnx for ur explanation, but the answer I got using ur method is the same as I got before (592.9 kg), which is inconsistent with the 790 kg answer listed on the back of the book.
Perhaps you should show your work, and make sure your units are correct.
 

1. How do you estimate a polar bear's mass using flotation?

The most common method used to estimate a polar bear's mass through flotation is by measuring the bear's displacement in water. This involves placing the polar bear in a tank of water and recording the amount of water that is displaced. The displaced water is then weighed to calculate the bear's mass.

2. What factors can affect the accuracy of estimating a polar bear's mass through flotation?

Some factors that can affect the accuracy of estimating a polar bear's mass through flotation include the bear's behavior in the water, such as whether it is actively moving or trying to escape, as well as the temperature and salinity of the water. Additionally, the accuracy of the equipment used and the skill of the researcher can also impact the results.

3. Are there any alternative methods for estimating a polar bear's mass?

Aside from flotation, other methods for estimating a polar bear's mass include using body measurements and equations based on the bear's size and shape, as well as using remote sensing techniques such as aerial photogrammetry or thermal imaging. These methods may not be as accurate as flotation, but can still provide a reasonable estimate of the bear's mass.

4. How can estimating a polar bear's mass through flotation benefit conservation efforts?

Knowing the mass of a polar bear can provide valuable information for conservation efforts, such as monitoring changes in body condition due to climate change or assessing the effectiveness of management strategies. It can also help researchers understand the energy requirements of polar bears and inform conservation plans for their prey species.

5. Are there any limitations to estimating a polar bear's mass through flotation?

One limitation of estimating a polar bear's mass through flotation is that it can only be done on captive or sedated bears, as it is not safe to approach wild bears in their natural habitat. This can limit the sample size and may not accurately represent the entire polar bear population. Additionally, the technique may not be suitable for bears with certain health conditions or irregular body shapes.

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