Density of Log: Find Area Exposed & Calculate kg/m3

[dstarnes]

Homework Statement

A round wooden log with a diameter of 83 cm floats with 72% of its radius out of the water. What is the log's density?
answer unit is kg/m3

Homework Equations

density of water= 1000 kg/m^3

The Attempt at a Solution

I've tried to find the area that is exposed, but do not know where to go from there.

 

[berkeman]

Think about it in terms of bouyancy (sp?). Anything that floats like a boat or a log, does so because the volume of the water displaced has a weight that is equal to the weight of the object. So the whole weight of the log is equal to the weight of the water displaced by the partial cylinder that is under water. Use the facts in the problem statement to tell you what that volume portion would be, and go from there...

 

[dstarnes]

ok i kind of understand what you are saying, but wanted some clarification on something. All right how am i to determine what the volume of the submerged part of the log is.

 

[OlderDan]

ok i kind of understand what you are saying, but wanted some clarification on something. All right how am i to determine what the volume of the submerged part of the log is.

One way to do this is to think of the exposed area of the end of the log (a segment of a circle) as a sector (pie slice) of a circle with an isosceles triangle cut off. You can figure out the angles of the triangle and find the area of a segment as a fraction of the area of a circle, then subtract the area of the triangle. Then again you could look up the area of a segment, or use calculus to compute it.