Specific Gravity

[pm1]

What is the specific gravity for a 5.0 mL object that weighs 32 N in air and 20 N in water?

A. 2.40
B. 2.67
C. 4.00
D. 6.40

Answer: B

I now get it.. was able to solve it by realizing that the volume is the same. And solving by V=12/pliquid and V=32/pobject

However, when I was doing the problem I mistakenly did m/V and then divided it by density of water.

I guess I was thrown off by the 5.0mL.

Why is it not correct to do it this way? 3.2kg / 5 mL ?

Thank you!!!

---

Members don't see this ad.

 

[doy]

hmmm it seems to me the numbers are off?

Because you are correct in
SG=density object/density water which is just density of object =6.4
but also
SG=Weight of object/Buoyant force, which would be 32/12 -->2.67

I think the numbers are wrong here

 

[pm1]

hmmm it seems to me the numbers are off?

Because you are correct in
SG=density object/density water which is just density of object =6.4
but also
SG=Weight of object/Buoyant force, which would be 32/12 -->2.67

I think the numbers are wrong here

what do you mean by the number being off?

I guess I will just stick with the weight of the object/bouyant force..

thank you

 

[doy]

what do you mean by the number being off?

I guess I will just stick with the weight of the object/bouyant force..

thank you

As in they don't match up when doing the calculations in two different ways.Perhaps it was just telling us that the object occupies 5 mL and not that all of the 5 mL is submerged.

Anyone else want to chime in on this?

 

[Zyto]

The numbers aren't wrong. Here's how I solved it. It's definitely not as easy as weight/buoyant force but it helps explain the difference between your first and second answer.

Calculations:

(Vobject)(Density water)(Gravity) = 12. Density of the water is constant (1000kg/m^3), we are given the volume of the object. Just for kicks, lets solve for gravitational acceleration (g).

(5*10^-6 m^3)(1000 kg/m^3)(g) = 12 kgm/s^2 (1N = 1kg/m/s^2)

That gives us g = 2.4 * 10^3 m/s^2 .... I guess we aren't on Earth!

Solve for the mass in air of the object using new g and the given weight of the object, 32N.

32N = mass * 2400 m/s^2

mass = 1/75 kg or .01333 kg

Now, solve for the density of the object.

density = mass/volume

= .01333kg/(5*10^-6 m^3)

= 2,666 kg/m3.

To get the specific gravity (density object/ density water):

(2,666 kg/m^3)(1000kg/m^3) = 2.67.

This problem had some annoying math, but it is a little intuitive (12/5 = a little less than 1/5, etc). The danger is in trying to calculate mass from weight. When we aren't told what type of gravitational force we are dealing with mass could be anything. This would have caught me if my physics teacher didn't consistently try to confuse us by using values of g that arent -9.8m/s^2 in questions that did not give the value of g.

 

[gettheleadout]

Yeah the question doesn't specify that the object is submerged when in water, so I wouldn't assume we can use the ratio of the densities = W / B.

 

[pm1]

Yeah the question doesn't specify that the object is submerged when in water, so I wouldn't assume we can use the ratio of the densities = W / B.

thank you for the answers!

but if it wasn't submerged in water how were we able to solve it by counting the volume as the same and it gives the right answer?

I did..

Fb= 32-20 = 12 = pliquid vsubmerged g

Weight= 32 = pobject vobject g

then, by assuming that v was the same I solved for v.

v=12/pliquid g
v=32/pobject g

pobject / pliquid = 32/12

and that gives 2.67

 

[gettheleadout]

thank you for the answers!

but if it wasn't submerged in water how were we able to solve it by counting the volume as the same and it gives the right answer?

I did..

Fb= 32-20 = 12 = pliquid vsubmerged g

Weight= 32 = pobject vobject g

then, by assuming that v was the same I solved for v.

v=12/pliquid g
v=32/pobject g

pobject / pliquid = 32/12

and that gives 2.67

I didn't say that it wasn't submerged, just that the problem didn't say it was. But actually, since all the answer choices are densities greater than that of water, we can infer that it's submerged by looking at them and then use the W / B relationship.

 

[gettheleadout]

The numbers aren't wrong. Here's how I solved it. It's definitely not as easy as weight/buoyant force but it helps explain the difference between your first and second answer.

Calculations:

(Vobject)(Density water)(Gravity) = 12. Density of the water is constant (1000kg/m^3), we are given the volume of the object. Just for kicks, lets solve for gravitational acceleration (g).

(5*10^-6 m^3)(1000 kg/m^3)(g) = 12 kgm/s^2 (1N = 1kg/m/s^2)

That gives us g = 2.4 * 10^3 m/s^2 .... I guess we aren't on Earth!

Solve for the mass in air of the object using new g and the given weight of the object, 32N.

32N = mass * 2400 m/s^2

mass = 1/75 kg or .01333 kg

Now, solve for the density of the object.

density = mass/volume

= .01333kg/(5*10^-6 m^3)

= 2,666 kg/m3.

To get the specific gravity (density object/ density water):

(2,666 kg/m^3)(1000kg/m^3) = 2.67.

This problem had some annoying math, but it is a little intuitive (12/5 = a little less than 1/5, etc). The danger is in trying to calculate mass from weight. When we aren't told what type of gravitational force we are dealing with mass could be anything. This would have caught me if my physics teacher didn't consistently try to confuse us by using values of g that arent -9.8m/s^2 in questions that did not give the value of g.

It definitely is that easy.

Given that d_obj / d_water = specific gravity = weight / buoyant force, the value of g is irrelevant because it cancels out. The buoyant force is the apparent weight loss of the object in water, so its 32 - 20 = 12 N.

Ergo, specific gravity = 32 / 12 = 8/3 = 2.67. B.

If you assume earthly gravitational acceleration and try to calculate the mass of the object from its air weight and find its density, you'll find that its density is 640 kg/L. The density of water is 1 kg/L, so the specific gravity would be 640, not 6.4. None of the answers are close, so this path should be abandoned at this point and the W / B relationship used.

 

[pm1]

It definitely is that easy.

Given that d_obj / d_water = specific gravity = weight / buoyant force, the value of g is irrelevant because it cancels out. The buoyant force is the apparent weight loss of the object in water, so its 32 - 20 = 12 N.

Ergo, specific gravity = 32 / 12 = 8/3 = 2.67. B.

If you assume earthly gravitational acceleration and try to calculate the mass of the object from its air weight and find its density, you'll find that its density is 640 kg/L. The density of water is 1 kg/L, so the specific gravity would be 640, not 6.4. None of the answers are close, so this path should be abandoned at this point and the W / B relationship used.

got it! Thank you guys!!

 

[Zyto]

It definitely is that easy.

Given that d_obj / d_water = specific gravity = weight / buoyant force, the value of g is irrelevant because it cancels out. The buoyant force is the apparent weight loss of the object in water, so its 32 - 20 = 12 N.

Ergo, specific gravity = 32 / 12 = 8/3 = 2.67. B.

If you assume earthly gravitational acceleration and try to calculate the mass of the object from its air weight and find its density, you'll find that its density is 640 kg/L. The density of water is 1 kg/L, so the specific gravity would be 640, not 6.4. None of the answers are close, so this path should be abandoned at this point and the W / B relationship used.

You misunderstood what I meant by "it's not that easy".

What I'm trying to say is that the way I solved it was not as easy as the quick way of dividing the weight by the buoyant force. It does, however, show why you can't divide the weight of the object by g of =10m/s^2, and then divide by the given volume to get a quick (wrong) answer.

 

[gettheleadout]

You misunderstood what I meant by "it's not that easy".

What I'm trying to say is that the way I solved it was not as easy as the quick way of dividing the weight by the buoyant force. It does, however, show why you can't divide the weight of the object by g of =10m/s^2, and then divide by the given volume to get a quick (wrong) answer.

Ah, I see. I thought you were referring to the problem itself. My bad.

 

[BerkReviewTeach]

but also
SG=Weight of object/Buoyant force, which would be 32/12 -->2.67

I seriously don't want this to sound like a plug, because that is not at all what it's meant to be. But I have to say that these questions used to stress me out and I felt I had to do them the long way until I learned the BR method you just referenced. Seriously makes this type of question an easy one.

Because the object has a weight in water, it's denser than water and thus is a sinker.

For sinkers, the density_object/density_medium = W/B.

In water, the SG is density_object/density_medium, so for this questions it's so simple to get the answer. Weight is 32 N and B is (32 - 20) N.

 

[doy]

I seriously don't want this to sound like a plug, because that is not at all what it's meant to be. But I have to say that these questions used to stress me out and I felt I had to do them the long way until I learned the BR method you just referenced. Seriously makes this type of question an easy one.

Because the object has a weight in water, it's denser than water and thus is a sinker.

For sinkers, the density_object/density_medium = W/B.

In water, the SG is density_object/density_medium, so for this questions it's so simple to get the answer. Weight is 32 N and B is (32 - 20) N.

Yeah I definitely pulled out the BR method for SG. And for pretttty much anything else.

Also, it's nice to know that we shouldn't assume we are not on Earth! I guess that's what my "numbers being off" statement really meant haha.