Finding the Density of a Duck Floating on a Lake

[MKM]

A duck is floating on a lake with 28% of its volume beneath the water. What is the average density of the duck?
This question seems pretty straight froward I realize ultimately that in order to find the answer the duck density= duck mass/duck V. If it is 28% I am assuming that should equal .28V and I know I need to use the formula for bouyant force FB=Weight of fluid=density of fluid x Volume of fluid x g I can plug in the density of fluid but I am not sure how to find all of the other variables having only been given a percentage of the Volume.

 

[BerryBoy]

You said that the bouyancy force is equal to the the weight of water displaced. So what is the force oppossing this?

i.e. Can you write the weight of the duck in terms of it's density and volume?

Regards,
Sam

 

[MKM]

I think its W= density .28V x 9.8

 

[dx]

Lets say the volume of the duck is one(this assumption won't change anything since the density of the duck doesn't depend on its mass, it will sink 28% of its volume no matter what its volume is). then the volume beneath water is 28/100. The mass of the duck times g will be equal to the density of water times 28/100 times g.

$$M\times{9.8} = d_{w}\times{0.28}\times{9.8}$$

Now, the volume is $$\frac{M}{V} = M$$

 

[BerryBoy]

I think its W= density .28V x 9.8

Almost, its whole mass is going to give it weight, think about your V term.
Tip: Always write algebra until the end, just in case things cancel (especially g).

So you have:

$$W=?=Bouyancy=\rho_{watter}V_{water}g$$

You also know:
$$V_{water}=0.28V_{duck}$$

Now, the volume is
$$\frac{M}{V}=M$$

Surely a typo !??

Regards,
Sam

 

[BerryBoy]

Can you take it from here?