Specific Gravity question

[sshah92]

---

Members don't see this ad.

Hey all,

So I've recently been improving drastically on PS after massive amounts of content review but am still pressed for time every time I take a practice test. Questions like this one drag me down the most. I need help with understanding this question on a conceptual level, but I'll post my derivations here as well:

"An object with 15 grams mass is immersed in benzene and suffers an apparent loss of mass of 5 grams. What is the approximate specific gravity of the object? (Data: Specific gravity of benzene = 0.7)."

So Fnet = Fapp = Fg - Fb = M(obj)*g - (rho, liquid)g*V(submerged)

Divide both sides by g to get apparent mass, M(obj) - (rho,liquid)*V(submerged)

Isolate (rho)object to equal M(object)*(rho,liquid) / M(object) - M(apparent) = (15*.7)/(15-10) = 2.1

This honestly took me FOREVER. I missed it on the practice exam and it took me a while to figure out while reviewing. A couple of things are confusing me. First of all, I think of "apparent loss in mass" as what's left on a scale after subtracting buoyant force from weight in air. But while deriving the answer I found that in order to get to the answer, 2.1, I have to think of apparent loss in mass as "buoyant" mass, or 10 grams. Why is this?

Help would be greatly appreciated!

 

[BerkReviewTeach]

But while deriving the answer I found that in order to get to the answer, 2.1, I have to think of apparent loss in mass as "buoyant" mass, or 10 grams. Why is this?

Help would be greatly appreciated!

Weigh yourself in air and then weigh yourself in water. You appear to weigh less in water because of the buoyant force that holds you up (opposes gravity). Thus, we often think of the buoyant force as your apparent weight loss when you weigh an object immerced in that medium.

The other thing that will help immensely on these types of questions is to employ the BR method. First decide if the object either (a) sinks or (b) floats in the medium. In this case the object is denser than benzene, so it will sink. For an object that sinks in a medium, we use the shortcut relationship:

^W/_B = ^rhoobject/_rhomedium​

In this case, the ratio of 15/5 = density of object/0.7, so the density of the object is 3 x 0.7 = 2.1. The specific gravity is the density of the object divided by the density of water, which we take to be 1 (unless told otherwise), making 2.1 your answer.

This is about as simple a method as you could want, and buoyancy questions should take no more than twenty seconds.

 

[dcnetsfan77]

Hey, was wondering if you could clarify your answer here because I am having trouble reading the formula you used up there^....also if the object floated what would you change in your approach?

thanks

 

[dcnetsfan77]

Hey, was wondering if you could clarify your answer here because I am having trouble reading the formula you used up there^....also if the object floated what would you change in your approach?

thanks

Weigh yourself in air and then weigh yourself in water. You appear to weigh less in water because of the buoyant force that holds you up (opposes gravity). Thus, we often think of the buoyant force as your apparent weight loss when you weigh an object immerced in that medium.

The other thing that will help immensely on these types of questions is to employ the BR method. First decide if the object either (a) sinks or (b) floats in the medium. In this case the object is denser than benzene, so it will sink. For an object that sinks in a medium, we use the shortcut relationship:

^W/_B = ^rhoobject/_rhomedium​

In this case, the ratio of 15/5 = density of object/0.7, so the density of the object is 3 x 0.7 = 2.1. The specific gravity is the density of the object divided by the density of water, which we take to be 1 (unless told otherwise), making 2.1 your answer.

This is about as simple a method as you could want, and buoyancy questions should take no more than twenty seconds.

Hey, was wondering if you could clarify your answer here because I am having trouble reading the formula you used up there^....also if the object floated what would you change in your approach?

thanks