Help with bouyancy problems...

[ravupadh]

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I always screw up these types of problems. Like when they tell you that "An object with a mass of 34 grams is immersed in benzene and apparently loses 14 grams. What is the specific gravity of the object? (Benzene spec. grav. = 0.7).)"

How do I go about approaching this type of problem? I know that p * V * g = mg but that's about it lol.

And for bouyancy force in general, does p(fluid) * V(displaced) * g ALWAYS equal mg when the object is floating as well as sinking?

Thanks.

 

[Axon hillock]

I always screw up these types of problems. Like when they tell you that "An object with a mass of 34 grams is immersed in benzene and apparently loses 14 grams. What is the specific gravity of the object? (Benzene spec. grav. = 0.7).)"

How do I go about approaching this type of problem? I know that p * V * g = mg but that's about it lol.

And for bouyancy force in general, does p(fluid) * V(displaced) * g ALWAYS equal mg when the object is floating as well as sinking?

Thanks.

When they say it loses 14g that is due to buoyancy force. So you set 14*g= Buoyancy force and solve for the volume of the object. Then you can solve for density and thus the specific gravity.

 

[exquisitemelody]

Do you know what the correct answer is?

 

[salim271]

I like to approach everything with as little math as possible (because I suxxorz at it.)

If the mass completely sunk just below the surface and stayed there, S.G mass = S.G benzene. If it floated halfway, S.G mass = S.G benzene - 1/2(S.G benzene) = 0.35, and since the compound sunk a little less than halfway, i would look for the answer that was a little less than 0.35.

 

[MShopes]

I always screw up these types of problems. Like when they tell you that "An object with a mass of 34 grams is immersed in benzene and apparently loses 14 grams. What is the specific gravity of the object? (Benzene spec. grav. = 0.7).)"

How do I go about approaching this type of problem? I know that p * V * g = mg but that's about it lol.

And for bouyancy force in general, does p(fluid) * V(displaced) * g ALWAYS equal mg when the object is floating as well as sinking?

Thanks.

Okay I will give you a formula to use in these equations. The formula is simply: (mass)/(mass-apparent mass)=density of object/density of fluid it is submerged in.

Apparent mass is 34-14=20 g.
real mass=34 g.

Density of fluid (benzene in this case) is 0.7 g/cm^3 since specific gravity of water is 1 g/cm^3. I got the density from the specific gravity formula (specific gravity (0.7)=density of benzene/density of water (1 g/cm^3)) and then solved for density of benzene. Now I have everything except the density of the object.

So (mass)/(mass-apparent mass)=density of object/density of fluid, (34)/(34-20)=density of object/0.7, density of object=1.7 g/cm^3. Since the density of the object is 1.7 g/cm^3, then the specific gravity is 1.7/1=1.7. So the specific gravity is 1.7 and that is the answer.

Correct me if I'm wrong but you always use that formula for these kind of problems.

 

[salim271]

Okay I will give you a formula to use in these equations. The formula is simply: (mass)/(mass-apparent mass)=density of object/density of fluid it is submerged in.

Apparent mass is 34-14=20 g.
real mass=34 g.

Density of fluid (benzene in this case) is 0.7 g/cm^3 since specific gravity of water is 1 g/cm^3. I got the density from the specific gravity formula (specific gravity (0.7)=density of benzene/density of water (1 g/cm^3)) and then solved for density of benzene. Now I have everything except the density of the object.

So (mass)/(mass-apparent mass)=density of object/density of fluid, (34)/(34-20)=density of object/0.7, density of object=1.7 g/cm^3. Since the density of the object is 1.7 g/cm^3, then the specific gravity is 1.7/1=1.7. So the specific gravity is 1.7 and that is the answer.

Correct me if I'm wrong but you always use that formula for these kind of problems.

The density of the object is less than the density of benzene isnt it? More of it is floating than sinking, so the specific gravity should be less too... are you sure it isnt Mass - apparent mass / mass = density object/density fluid?

 

[MShopes]

The density of the object is less than the density of benzene isnt it? More of it is floating than sinking, so the specific gravity should be less too... are you sure it isnt Mass - apparent mass / mass = density object/density fluid?

What makes you think more of it is floating than is sinking. I probably would think all of it sank...the fact that its mass became less than the real mass has nothing to do with floating...it actually means that the object that sank in the fluid weights less due to the force of buoncy pushing upward. However, it did not indicate whether it float completely or partially or it sank completely. And yes, I'm 100 % sure about this formula, I have my college textbook in front of me right now and it says the same exact formula.

 

[salim271]

What makes you think more of it is floating than is sinking. I probably would think all of it sank...the fact that its mass became less than the real mass has nothing to do with floating...it actually means that the object that sank in the fluid weights less due to the force of buoncy pushing upward. However, it did not indicate whether it float completely or partially or it sank completely. And yes, I'm 100 % sure about this formula, I have my college textbook in front of me right now and it says the same exact formula.

Okeedokey then ur right and im wrong ^_^ lol. I suck at physics.

 

[MShopes]

Okeedokey then ur right and im wrong ^_^ lol. I suck at physics.

LOL physics isn't my favorite subject either...but at least is better than verbal for me!

 

[ravupadh]

Wow yep that's the correct answer. I understand how you got the answer but can you explain the rationale behind the formula? ((mass)/(mass-apparent mass)=density of object/density of fluid )

Because I'm looking at my TBR book and the only formula they give for bouyancy is p V g = m g

Also, like I asked before is the bouyancy force always equal to = mg of an object even when the object is sinking as well as floating?

 

[bullsfan1986]

Wow yep that's the correct answer. I understand how you got the answer but can you explain the rationale behind the formula? ((mass)/(mass-apparent mass)=density of object/density of fluid )

Because I'm looking at my TBR book and the only formula they give for bouyancy is p V g = m g

Also, like I asked before is the bouyancy force always equal to = mg of an object even when the object is sinking as well as floating?

For questions like these (when the question doesn't explicitly say that the object is accelerating downward or upward) you can pretend that the object is stationary and then calculate for net force on the object.

Because you know that the buoyant force opposes the gravitational force you can set the equation up like: Fnet = mg - pVg...or ma= mg - pVg

You know that because your object isn't moving a=0 so 0 = mg-pVg which means that mg = pVg. (make sure to use m= apparent mass of the object)

The g's cancel out and you solve for V. Once you find V, take the actual mass of the object and divide by V. Hope that helps.

Remember, if the question specifically says that the object is accelerating upward or downward your net force would not be = 0.

 

[MShopes]

Wow yep that's the correct answer. I understand how you got the answer but can you explain the rationale behind the formula? ((mass)/(mass-apparent mass)=density of object/density of fluid )

Because I'm looking at my TBR book and the only formula they give for bouyancy is p V g = m g

Also, like I asked before is the bouyancy force always equal to = mg of an object even when the object is sinking as well as floating?

Alright first, I derived this formula from the very similar formula which is ((weight)/(weight-apparent weight)=density of object/density of fluid )

Say weight is the symbol W and the apparent weight is the simple W'.

W=mg=density of object* Volume of object *g (m = density*Volume)
W-W' (real weight-apparent weight)= FB (force of Buoyancy).....force of buoyancy is the force that causes the weight to be less that is why W-W'=FB.

So you have two equations so far.
W=mg=density of object* Volume of object * g
W-W'=FB, W-W'=density of fluid*Volume of fluid displaced*g. (Notice that FB is the density of FLUID and Volume of FLUID displaced not the density of object like in W=mg.

If you devide these two formulas you get, W/(W-W')=(density of object* V of object* g)/(Density of fluid*volume of fluid displaced* g).

By cancellations, you can cancel the g and the volume because volume of object is the same as the volume of fluid displaced by that object. You will be left with density on the right side and W/W-W' in the left side.

Sorry if I confused you but you asked me where I derived this equation from.

Notice that W=mg, so technically if we cancel the g, we can be left off with mass, and thus the formula of mass/mass-apparent mass is same as weight/weight-apparent weight and you can use either of them depending on the question. If the question gave you the weight in N then use the weight equation; if the quation give you the mass like this one, then use the mass formula...simple as that.

And to your last question, the buoyancy force is equal to mg only when the object is sinking. The buoyancy force when the object is completely floating is 0. Think about it this way, the bouyancy force is the weight of the volume of fluid displaced by that object. So, if the object is completely floating, no volume of fluid will be displaced and thus the mass displaced will be 0 and hence there will be no force of buoyancy. In order to have force of buoyancy, at least a little bit of fluid has to be displaced by the object, so an object can be partially sinking and have a force of buoyancy because it displaced some volume. Notice that the mass of mg is not the mass of the object but the mass of fluid displaced. Since it doesn't seem much logical to measure the mass of fluid, we measure volume* density and substitute it for mass...but the volume here is the volume of FLUID displaced as well as the density of the fluid not the object.


P.S, this formula that I gave you isn't very common and I bet almost no prep book can include it. It can be derived from other formulas like I showed above but time sucks on the MCAT to be able to derive such equation quickly.


Sorry for my long post....if anything else, feel free to ask.

 

[MShopes]

For questions like these (when the question doesn't explicitly say that the object is accelerating downward or upward) you can pretend that the object is stationary and then calculate for net force on the object.

Because you know that the buoyant force opposes the gravitational force you can set the equation up like: Fnet = mg - pVg...or ma= mg - pVg

You know that because your object isn't moving a=0 so 0 = mg-pVg which means that mg = pVg. (make sure to use m= apparent mass of the object)

The g's cancel out and you solve for V. Once you find V, take the actual mass of the object and divide by V. Hope that helps.

Remember, if the question specifically says that the object is accelerating upward or downward your net force would not be = 0.

Wait what? So once you find V, and you take the actual mass and divide by V then it is going to give you the same density that you used in the first place to get the V. You went back again to the same thing. Doing like you said gave me a density of 0.7 which is what I used to get the volume. You realize that there is only one volume in this whole problem? This volume is the volume of fluid displaced or the volume of the object which is the same thing. And isn't the apparent mass=20 g? then why would you switch and use the actual mass to get the density if you used the apparent mass right before it. I'm not trying to oppose you but your way does not seem logical to me even though your approach concerning forces is absolutely correct. However, you are assuming it is not accelerating. Well, you don't know for sure if it is accelerating or not to assume the net force is 0. And I tried your way and it gave me the wrong answer.

 

[bullsfan1986]

Wait what? So once you find V, and you take the actual mass and divide by V then it is going to give you the same density that you used in the first place to get the V. You went back again to the same thing. Doing like you said gave me a density of 0.7 which is what I used to get the volume. You realize that there is only one volume in this whole problem? This volume is the volume of fluid displaced or the volume of the object which is the same thing. And isn't the apparent mass=20 g? then why would you switch and use the actual mass to get the density if you used the apparent mass right before it. I'm not trying to oppose you but your way does not seem logical to me even though your approach concerning forces is absolutely correct. However, you are assuming it is not accelerating. Well, you don't know for sure if it is accelerating or not to assume the net force is 0. And I tried your way and it gave me the wrong answer.

Sorry, I meant m= the difference between the mass and apparent mass.

 

[MShopes]

Sorry, I meant m= the difference between the mass and apparent mass.

You are absolutely correct. I noticed your way is actually more or less derived from that equation I gave or it is very similar to it but divided into parts. I did the calculations using your way and it is right as well. Good job!

 

[exquisitemelody]

OP, was this question originally in TBR or a practice mcat? I've seen that question before, but I'm not sure where...

 

[MShopes]

OP, was this question originally in TBR or a practice mcat? I've seen that question before, but I'm not sure where...

It better be not on a practice MCAT because I think this question would take more than a minute to solve it because of the math involved as well as the concept. It takes a little bit to see which equation to use and how to apply it correctly. I'm not sure...

 

[Axon hillock]

It better be not on a practice MCAT because I think this question would take more than a minute to solve it because of the math involved as well as the concept. It takes a little bit to see which equation to use and how to apply it correctly. I'm not sure...

Definitely a possible MCAT question. I've seen it on the practice tests. It's easy once you practice on a few problems.

 

[MShopes]

Definitely a possible MCAT question. I've seen it on the practice tests. It's easy once you practice on a few problems.

It isn't hard for me at all because I knew which formula to apply right away but for other people who don't know which formula to apply right away, it can take a little bit of time. Other type of problems like this might be a little bit of a problem for me. BTW, I love your name, isn't that where the action potential is generated? 😀

 

[Axon hillock]

It isn't hard for me at all because I knew which formula to apply right away but for other people who don't know which formula to apply right away, it can take a little bit of time. Other type of problems like this might be a little bit of a problem for me. BTW, I love your name, isn't that where the action potential is generated? 😀

Yep. Good studying🙂

 

[MShopes]

Yep. Good studying🙂

Thank you Axon Hillock, please don't forget to transmit the signal down there to me...I'm by the corner of the synapse waiting for the signal.....😀 Jokin

 

[Pre-Med Village]

Buoyant force problems are simple. The buoyant force is simple. Archimedes principle. The buoyant force equals the weight of the fluid displaced whether gas or liquid.

In my experience, where students lose track is in not realizing there are two basic problem types.

The first basic problem type is the SUBMERGED object. In those cases, start your thinking with the VOLUME. Compute the buoyant force by asking yourself how much weight of the fluid in which it is submerged the volume of the object displaces. With gaseous contents, such as helium or partial vacuum. Put that in the weight just as if they were ultra light cork. Generally it's simple derivation of a free body diagram from the weight of the object vector and the buoyant force vector to find the net force on the object. From such a free body diagram you can easily see that the specific gravity, the ratio of the density of the object to water, is why some objects rise to the surface of a pond when submerged and some sink.

The second basic problem type is the FLOATING object. Don't think volume of displaced fluid to find the buoyant force first. Think of the ENTIRE WEIGHT OF THE OBJECT. If the object if floating the buoyant force and the weight must be in equilibrium so the weight of the object will tell you the buoyant force exactly. If the object isn't very dense at all only a portion of its own volume is sufficient to displace enough fluid to weigh as much as the entire weight vector and produce the phenomenon of floating. In the second problem type, the case of the floating object, the fluid must have a higher density to make something float because only a portion of the object's volume is sufficient to displace an amount of fluid equal to the objects's weight.

Buoyant force is an upward force equal to the weight of the fluid displaced. In summary with submerged objects think first about the volume of the object. With floating objects think first about the weight of the partially submerged object and develop the force equilibrium of the weight and buoyant force. If you think about it for one second and it becomes clear that the ratio of volume submerged to total volume of the floating object must equal the specific gravity then you have this situation pretty well figured out I think.