A man is marooned on an island after his plane crashes into the ocean. After living couple of years, far away from home, his girlfriend, and any human contact, he decides to make a raft using the logs available in the island in hope of going home.
His current mass is 55kg due to malnutrition. Assume each log is 2m long with a radius of 0.05m and the density is 700 kg/m^3. Find the minimum number of logs he must fetch.

Question

A man is marooned on an island after his plane crashes into the ocean. After living couple of years, far away from home, his girlfriend, and any human contact, he decides to make a raft using the logs available in the island in hope of going home. 
His current mass is 55kg due to malnutrition. Assume each log is 2m long with a radius of 0.05m and the density is 700 kg/m^3. Find the minimum number of logs he must fetch.

anonymous · Answer

can u give me a medal

ganeshie8 · Answer

seems to me you know how to solve this problem :)

anonymous · Answer

Can someone please solve this?
Find the remainder when 11!+9! (999*8!) is divided by 18*7!-14*6! (2*8!) ?

anonymous · Answer

Depends on how wet the man wants to get

ganeshie8 · Answer

He is desperate, wants to go home somehow... so anything that keeps him from sinking down will do here...

parthkohli · Answer

for floatation,
the average density of the man+raft system < the average density of water

ganeshie8 · Answer

we can't get density of man right ?

parthkohli · Answer

yeah, that's a big problem. what we can do is just find the volume of the raft, and the combined mass of both, and divide them.

parthkohli · Answer

that wouldn't be the correct answer but I can't imagine any other way of doing this

astrophysics · Answer

$$M= \rho A h, V = Ah$$

ganeshie8 · Answer

is there a way to work this using forces
because it might be easy to convert density/mass/volumes to forces

ganeshie8 · Answer

i think we just need to balance the vertical forces, 
but i could be wrong.. there may be more to this problem..

parthkohli · Answer

The buoyant force is$$V\rho_{\rm liq} g$$The gravitational force is$$mg = V\rho_{\rm system} g $$So$$\rho_{\rm liq} \ge \rho_{\rm system}$$

astrophysics · Answer

That was the mass of the body and the volume of the water, so the forces acting on the body are gravity and the water pushing the body up

astrophysics · Answer

Thinking oscillations

parthkohli · Answer

the motion in reality is oscillatory because of added viscous force

parthkohli · Answer

^ i haven't studied oscillations yet but that's what I feel

ganeshie8 · Answer

$$V_{liq} = V_{logs}$$

is it ?

ganeshie8 · Answer

because, the volume of displaced liquid must equal  the volume of the logs

parthkohli · Answer

yeah!

anonymous · Answer

The easiest case to look at would be when the raft is just buoyant enough to keep the man out of the water, in which case the man does not contribute to the buoyant force, only the weight. This way you would not need to know his density. At this point, you also know that the log volume is equal to the volume of water displaced.

If you wanted the man to be a certain level above the water for more comfortable travels, you would have to adjust these volumes. If the man is desperate enough to sit in a bit of water, you could approximate his density (assuming he is very well hydrated on the islands coconuts) to be that of water. In reality, he would have very little fat on him and would be a bit more dense than water, but that is another problem altogether.

ganeshie8 · Answer

oh so we can forget about volume of man as he has to stay above the water ?

parthkohli · Answer

exactly!

anonymous · Answer

unless you would like to consider the negligible buoyant force that our atmosphere provides

ganeshie8 · Answer

|dw:1447829767780:dw|