When a crown of mass 14.7 kg is submerged in water, an accurate scale reads only 13.4 kg. Is the crown made of real gold?

Question

Ok How do I do this problem

I set up my free body diagram

Net Force = ma = 0= Ft + Fb - Fg

were Ft is the force of tension on the scale that was used to measure it's apparent weight

- Ft = Fb - Fg
Ft = Fg - Fb
Ft = (mass of object)g - (density of fluid)g(volume of fluid)

density of object = (mass of object)/(volume of object)

mass of object = (density of object)(volume of object)

plug chug

Ft = (density of object) (volume of object)g - (density of fluid)g(volume of fluid)

ok were do I go from here I think that the volumes are suppose to be the same but I do not see how.

Answer 1

IF the thing is submerged, then

volume=mass/densitymaterial

The bouyant force is volumedisplaced*denstitywater.

bouyantforce= 14.7/densitymaterial*density water.

according to the measurements, the bouyant force is 14.7-13.3=1.4g

then calculate the density of material:

density material= 14.7/1.4 * 1g/cm^3
which is about 10.5g/cm^3 So is this Gold?

Answer 2

why are the volumes the same

Answer 3

Fg on object = (it's density)(it's volume)g

Fb = (density of water)(volume of water underneath object pushing it up)gravity

your suppose to divide the two gravity is suppose to cancel out and the volume but the volumes are two different objects why are they the same

Answer 4

What objects do you know when submerged change volume? Certainly chunks of metal do not.

Answer 5

9.8