How to Solve a Buoyancy Problem: A Step-by-Step Guide

[new324]

Buoyancy problem, please check my work :)

Can you check my work here?

A crown is weighed in air and submerged in water. The scale reads 7.84 N in air and 6.86 N in water.
find (a) the buoyant force (b) the volume of the crown (c) the density of the crown (d) is the crown made of gold?

(a) 7.84-6.86=.98 N
(b) Bouyant force=Volume(submerged object)*density(liquid) *gravity
so .98=v*1000*9.8 V=.0001 m^3 (=.1 cm^3)
(c) Density Object= (Weight object/Bouyant Force)*Density Liquid
p=(7.84/.98)1000 ;p=8000 kg/m^3
(d) I'm not sure the density of gold, I think its more than double this density though. So No, the crown is not made of Gold.

Thanks for any help!

 

[Chen]

Looks good to me!

Quick search shows that "A cubic centimetre of gold will weighs 19.3 grams" so that makes the gold density 19,300 kg/m³.

By the way, you don't have to use this equation to find the object density:

$$\rho _o = \frac{W_o}{B}\rho _l$$

It's correct but the dependency on the density of the liquid is not needed, since:

$$B\rho _o = W_o\rho _l$$

$$\rho _lv_og\rho _o = m_og\rho _l$$

So the liquid density cancels and you get:

$$v_o\rho _o = m_o$$

Which is (amazingly :tongue:) exactly the defintion of mass density. You have the object's mass, since you know its weight in air.

 

[Doc Al]

Looks good to me.

(a) 7.84-6.86=.98 N

Right.

(b) Bouyant force=Volume(submerged object)*density(liquid) *gravity
so .98=v*1000*9.8 V=.0001 m^3 (=.1 cm^3)

Right. (But 1 m^3 = 1,000,000 cm^3)

(c) Density Object= (Weight object/Bouyant Force)*Density Liquid
p=(7.84/.98)1000 ;p=8000 kg/m^3

Right. Though I'm used to the simpler "Density = Mass/Volume", what you've done is equivalent.

(d) I'm not sure the density of gold, I think its more than double this density though. So No, the crown is not made of Gold.

Right. The density of gold is about 19,300 Kg/m^3

Note: Chen, you beat me again!

 

[Chen]

Tsk tsk.

 

[Doc Al]

Tsk tsk.

I'm getting old and slow, I guess.

 

[Chen]

We both even said "Looks good to me". :tongue:

mmmkay, enough monkey business now, got to get back to studying Bible again.

 

[new324]

Awesome. Thanks a lot Chen and Doc Al. It's a great thing when people compete over helping you first. Haha. Thanks again.