How many people before it sinks

[superjen]

A raft is made of 9 logs lashed together. Each is 29.1 cm in diameter and has a length of 5.7 m. How many people can the raft hold before they start getting their feet wet. Assume the average person has a mass of 69.3 kg and that the density of water and wood is 1000 kg/m3 and 600 kg/m3, respectively

All i know iss

FB = mpg + mrg
i don't really know how to figure it out from here!

 

[mgb_phys]

A floating object displaces water equal to it's weight.
So how much mass of water would be displaced if the logs were completely submerged (hint volume of logs and density of water)
Now how much do those logs alone weigh - and so how much extra weight of people could be added.

 

[redargon]

can you define your variables, it will help us to answer your question too? ie. what is FB and mpg and mrg?

Remember that the force of bouyancy is related to the volume of the liquid that is displaced.

Don't forget to find out the mass (and weight) of all the logs.

Drawing a diagram (Free body diagram) with force arrows will also help.

 

[redargon]

mgb_phys beat me to it.

 

[Carid]

People will start to get their feet wet when the logs are just underwater and the people aren't. So the upthrust due to the logs will be equal to the weight of the logs and of the people standing on them.

Upthrust = weight of water displaced = log volume * water density

DownForce = weight of logs + weight of people

Our condition is Upthrust = DownForce