How to Solve a Buoyancy Problem

In summary, a crown was weighed in air and submerged in water to find its buoyant force, volume, density, and composition. The calculations showed that the crown had a buoyant force of 0.98 N, a volume of 0.0001 m^3, and a density of 8000 kg/m^3, indicating that it is not made of gold. The density of gold was also determined to be 19,300 kg/m^3.
  • #1
new324
30
0
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!
 
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  • #2
Looks good to me! :smile:

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:

[tex]\rho _o = \frac{W_o}{B}\rho _l[/tex]

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

[tex]B\rho _o = W_o\rho _l[/tex]

[tex]\rho _lv_og\rho _o = m_og\rho _l[/tex]

So the liquid density cancels and you get:

[tex]v_o\rho _o = m_o[/tex]

Which is (amazingly :-p) exactly the defintion of mass density. :smile: You have the object's mass, since you know its weight in air.
 
Last edited:
  • #3
Looks good to me.
new324 said:
(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! :mad:
 
  • #4
Tsk tsk. :wink:
 
  • #5
Chen said:
Tsk tsk. :wink:
I'm getting old and slow, I guess. :biggrin:
 
  • #6
We both even said "Looks good to me". :-p

mmmkay, enough monkey business now, got to get back to studying Bible again. :frown:
 
  • #7
Awesome. Thanks a lot Chen and Doc Al. It's a great thing when people compete over helping you first. Haha. :biggrin: Thanks again.
 

FAQ: How to Solve a Buoyancy Problem

What is the concept of buoyancy?

Buoyancy is the upward force exerted by a fluid on an object that is partially or fully submerged in the fluid. It is a result of the difference in pressure between the top and bottom of the object.

How do you calculate the buoyant force?

The buoyant force can be calculated by multiplying the density of the fluid by the volume of the displaced fluid and the acceleration due to gravity. This can be represented by the equation Fb = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

What factors affect buoyancy?

The buoyancy of an object is affected by its volume, density, and the density of the fluid it is submerged in. Objects with larger volumes and lower densities will experience greater buoyant forces, while objects with smaller volumes and higher densities will experience smaller buoyant forces.

How does the shape of an object affect its buoyancy?

The shape of an object can affect its buoyancy because it can change the volume of the displaced fluid. For example, a hollow object will displace more fluid than a solid object of the same size, resulting in a greater buoyant force.

Can an object float in a fluid with a higher density?

No, an object will only float in a fluid if its density is less than the density of the fluid. If the object's density is greater than the density of the fluid, it will sink. However, an object can be partially submerged and experience a net upward force due to buoyancy if its density is only slightly higher than the density of the fluid.

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