EK Physics Lecture 3: Displaced Mass and Specific Gravity

[mcatjelly]

Would anyone be willing to walk me through/explain the solution to #51 of the 3rd 30 minute Physics exam? I know this is a pretty basic concept, but I'm just not comprehending what they're telling me, haha. I would be so happy if the MCAT was math-less.

Q: A 2 kg object submerged in the unknown fluid [with spec. gravity of 5.0] has an apparent loss of mass of 0.5 kg. What is the specific gravity of the object?

A. 1
B. 1.25
C. 5
D. 20

A: The volume of the fluid displaced by the object is equal to the volume of the object. The mass of the fluid displaced by the object is equal to the apparent loss of the object (weight = 5 N). Since the specific gravity of the fluid is 5, the same volume of water would weight 1/5 as much or 1 N. Thus, the object weighs 20 times more than water giving it a specific gravity of 20.

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[lifetothefullest]

The specific gravity of a substance is defined as the density of the object divided by the density of water. So what you want to find is the density of the object since the density of water is defined as 1 g/mL. Density is mass divided by volume. You know that the object weighs 2 kg. You don't know the volume, though. But you do know that the mass of the object is diminished by 0.5 kg upon placing it in fluid. That means it displaced 0.5 kg of fluid by Bernoulli's principle. Now you're almost done. If the fluid was water, you'd know that the volume displaced would be 500 mL. But the fluid isn't water. It's actually 5 times more dense than water because, as outlined above, specific gravity is the density of the stuff divided by the density of water. Since the fluid has a specific gravity of 5, that means it's 5 times more dense than water, or 5 g/mL or 5 kg/L. So now you know that your object, which weighs 2 kg, displaced 0.5 kg of fluid, which translates directly to 0.1 L of fluid. So your density is 2 kg/0.1 L, or 20 g/mL. Specific gravity is density of the stuff divided by density of water, so 20 g/mL divided by 1 g/mL is 20.

 

[mcatjelly]

The specific gravity of a substance is defined as the density of the object divided by the density of water. So what you want to find is the density of the object since the density of water is defined as 1 g/mL. Density is mass divided by volume. You know that the object weighs 2 kg. You don't know the volume, though. But you do know that the mass of the object is diminished by 0.5 kg upon placing it in fluid. That means it displaced 0.5 kg of fluid by Bernoulli's principle. Now you're almost done. If the fluid was water, you'd know that the volume displaced would be 500 mL. But the fluid isn't water. It's actually 5 times more dense than water because, as outlined above, specific gravity is the density of the stuff divided by the density of water. Since the fluid has a specific gravity of 5, that means it's 5 times more dense than water, or 5 g/mL or 5 kg/L. So now you know that your object, which weighs 2 kg, displaced 0.5 kg of fluid, which translates directly to 0.1 L of fluid. So your density is 2 kg/0.1 L, or 20 g/mL. Specific gravity is density of the stuff divided by density of water, so 20 g/mL divided by 1 g/mL is 20.

Thank you, very helpful.

 

[ElectricNoogie]

Another way to arrive at the answer w/o calculation is to read the Q again, focusing on what they have told you happens. The object only lost 1/4 of its weight in the fluid, meaning it sinks into the fluid (Fbuoyant < Fg,). This implies that the object is more dense than the fluid it has been placed in and thus, will have a higher specific gravity (density object/density water) than the fluid. Only 1 answer here is > 5.

 

[mcatjelly]

Another way to arrive at the answer w/o calculation is to read the Q again, focusing on what they have told you happens. The object only lost 1/4 of its weight in the fluid, meaning it sinks into the fluid (Fbuoyant < Fg,). This implies that the object is more dense than the fluid it has been placed in and thus, will have a higher specific gravity (density object/density water) than the fluid. Only 1 answer here is > 5.

Also super helpful!

 

[NextStepTutor_3]

In general, MCAT questions like to use "apparent loss of weight" as a synonym for buoyant force, so "apparent loss of mass" * 10 will give you that value. After all, if an object seems like it weighs 5 N less in a fluid, that must be because a 5N upward force is pushing on it. Like the great answers said above, this is the same thing as the object (which weighs 20 N) displacing 5 N of fluid.

As for this exact question, I think people tend to get confused because it's easy to forget this object is NOT in water. We can fairly easily see that the object is 4x more dense than the fluid, since the 2kg of the object takes up the exact same volume as 0.5 kg of fluid. The key is that the specific gravity of the fluid is 5, so it's ALREADY 5x more dense than water on its own. This means our object is (5)(4) more dense than water, which gives us 20.