# Homework Help: Buoyant force concept question

1. Jul 28, 2010

### pookisantoki

I have been pondering about this for awhile now. If there are rocks on a boat (that's floating in a water) and one by one the rock is thrown onto the water. Does the water level rise or fall from the initial level?

I believe that it will rise but am not 100% sure.

2. Jul 28, 2010

### ehild

Why do you think so? Explain!

ehild

3. Jul 28, 2010

### pookisantoki

my reasoning is because of the forces acting on it....the Fb=density of the fluid * gravity * volume and by taking the rock out, were increasing the Fb so increasing the volume?

4. Jul 29, 2010

### ehild

Why do you think that Fb increases if you take the rock out? Fb=Volume of the immersed part of the boat*g*density of the fluid. Does an empty boat immerse deeper in the water or a loaded one?

ehild

5. Jul 29, 2010

### pookisantoki

loaded ones immerses deeper so Fb is less when the rocks are taken out so the volume would be less....?? thus the water level will decrease??

6. Jul 29, 2010

### Dick

Think of it this way. When the rock is in the boat, it's displacing a volume of water equal to its weight. When it's in the water it's displacing a volume of water equal to its volume. Think of what happens if the rock is really really dense.

7. Jul 29, 2010

### ehild

Yes. Let be the mass of the rock m, that of the boat is M. The boat floats, part of it of volume V1 is immersed in water. Fb = (M+m)g=ρ(water)*g*V1.

V1=(M+m)/ρ(water), the total occupied volume in the pond is V(water)+V1.*

You throw the rock into the water. The boat becomes lighter, Fb=Mg=ρ(water)*g*V2,

V2=M/ρ(water),

but the rock is on the bottom of the water, (assuming that its density is higher than that of the water) and its volume is

V(rock) = m/ρ(rock).

The total occupied volume in the pond is now

V2+V(water) +V(rock) **

When is the occupied volume bigger?

ehild