# Buoyancy of a raft

1. Jan 15, 2009

### chantalprince

1. The problem statement, all variables and given/known data

A raft is made of 11 logs lashed together. They are 38.0 cm in diameter and 6.10 m long and has a density of 700 kg/m^3. How many 60 kg persons can the raft hold in freshwater while keeping everybody's feet dry?

2. Relevant equations

Volume immersed/Volume total = density obj/ density fluid
% immersed= density obj/ density fluid
Bouyant force = roh x V x g
P = F/A (?)
m = roh x V

3. The attempt at a solution

I have found the volume of the raft: 2.42 cubic meters

Here are my thoughts: To keep everybody's feet dry, the raft can be immersed up to 99.9%. Not sure how to use the forumla above to my advantage... Also, I can find the bouyant force of the raft. Now, I'm stuck!

Thanks in advance to all who respond :)

Last edited: Jan 15, 2009
2. Jan 15, 2009

### LowlyPion

Re: Bouyancy-

Think of the volume of the logs as your budget. Figure the weight of the water displaced by that volume.

The first outlay from the budget is for the weight of the wood.

What's left over - volume times the density of that volume of water - is what you have in the bank to pay out then for additional weight.

So ... how many 60 kgs can you afford from your budget?

3. Jan 15, 2009

### chantalprince

Re: Bouyancy-

I can't quite wrap my mind around what your saying. However, if it's of any help to get me started, I think I found the weight of water displaced by the raft. I used: m = roh x V then used W = mg. Is this correct?

4. Jan 15, 2009

### LowlyPion

Re: Bouyancy-

That's the idea. Now you know the total of how much the logs and the people can weigh.

5. Jan 15, 2009

### chantalprince

Re: Bouyancy-

But I thought I just found the weight of the raft with the equations in my last reply... How do I find out the TOTAL weight I'm allowed??

6. Jan 15, 2009

### LowlyPion

Re: Bouyancy-

That's the whole point. The weight of the displaced water is what the logs will support. (After allowing for the weight of the logs themselves of course.)

7. Jan 15, 2009

### LowlyPion

8. Jan 15, 2009

### chantalprince

Re: Bouyancy-

Alright- so, I found the bouyant force, and then the weight of the raft, so the rest of the weight can go to people. So, what does the whole, "and not get their feet wet" bit have to do with this? Does it just mean that if we go over our "account balance" that the raft will sink? So, the raft will float up until the next person gets on?

9. Jan 15, 2009

### LowlyPion

Re: Bouyancy-

Yes. They don't want you getting into the density of the people and the volume they displace.

10. Jan 15, 2009

### chantalprince

Re: Bouyancy-

Ok :) Now another issue I am having. I took the force the raft can support, which is in newtons, as is the weight of the raft. So, how do I figure how many 60 kg persons this thing will hold? I thought it would be a simple conversion, but Im missing something somewhere. I did this:

(1 lb/4.448 N) (1kg / 2.2lb)

But- I still have newtons on top.

(Can you tell I SUCK at this physics stuff?)

11. Jan 15, 2009

### LowlyPion

Re: Bouyancy-

How many Newtons is a 60 kg person?

Hmmmm.... F = m*g = 60*9.8 = 588 N

12. Jan 15, 2009

### chantalprince

Re: Bouyancy-

Thank you so much for all of your help, LP