# Suspend Water

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**Hungover illusions - Water suspended no cup and balancing forks trick**

**Find density of a statue, by suspending it from a spring, in air and in water to give 28.4N and 17N, density?**

Full Question:

You are determining the density of a statue. When you suspend it from a spring scale, the scale measures 28.4N. When you completely immerse it in water, the scale reads 17.0N. What is the statue’s density?

Not sure how to tackle this one....

thanks heaps, thats great!

Well, let's see what we know. I guess you're supposed to consider the buoyant force in air also. So we don't know what the scale would measure in vacuum. It will be slightly more than 28.4 N.

The statue has a mass m, density d, volume V. The (unknown) weight in vacuum is mg.

In air, the buoyant force is the weight of the displaced air = (V*d_air)*g where d_air = density of air.

So mg - V*d_air*g = 28.4 N.

And in water, mg - V*d_water*g = 17 N.

Two equations for two unknowns m and V so this can be solved (d_air and d_water are constants that can be looked up). Subtract the 2nd equation from the 1st:

-V*d_air*g + V*d_water*g = 28.4 - 17 = 11.4

V(d_water - d_air)g = 11.4

V = 11.4/[ (d_water - d_air)*g ]

So that will give you V and you can plug it into either equation to get m. The density of the statue is m/V of course.

(edited)

Actually, I guess you don't need to worry about the density of air. If you assume that 28.4 N is the object's weight and air has a density of 0 (it's actually about 1/1000 that of water), the equations are:

mg = 28.4 N

mg - V*d_water*g = 17 N

So V = 11.4/( d_water*g)

And since m = 28.4 N/g

just plug in the values and calculate m/V.

It's late so I made this problem more complicated than it needs to be.