nc_nutcase said:
I used a diameter of 5” instead of 6” on the hollow part. If you go with 6” then it is the same as if you ignored the last 5” of the 25” long cylinder, which is obviously not correct, as we can see a little piece of wood there… I don’t know how exact my approach is, but it has to be close. As none of this wood is truly a geometrical shape, all calculations are approx.
ditto for me on the hollow bit. but you used a 4" inch radius on the cone-bit, whereas i used a 2". i did neglect that spar on the end since i didn't have any hard measurements on it. but since i'm betting the 25 inches is tip-to-tip, that portion is actually overestimated and included in the solid cylinder portion of the log.
nowadays we're taught to use pounds-mass (lbm) and pounds-force (lbf) as English units to distinguish between the concepts of force and mass (otherwise you're left with a sick feeling when asked to give the force exerted on a 5 pound mass accelerated 2 ft/s/s).
my fluids book does all the English measures in feet, so i went on ahead and did my work in cubic feet. the funky p is rho, or density (bet you knew that). the book gives the density of water at 80F as 62.1 lbm/cubic foot & the density of a soft wood is 32 lbm/cubic foot.
gravitaional acceleration is 32.17 ft/s/s, but since it is just operating as a conversion factor between force and mass, i notated it as lbf per lbm. when i was doing this, i was still uncertain about whether the typical scale measures force or mass, so i went on ahead and included it (which in retrospect, was unecessary
).
given that the displaced volume of water is equal to the volume of wood:
- Bouyant Force = density of water * gravity * displaced volume of water
and Weight = density of wood * gravity * volume of wood
Required Force = Bouyant Force - Weight
since 400 lbs seemed excessive for a peice of driftwood, i decided that scales measure mass. therefore i converted the required additional weight from pounds-force back to pounds-mass by dividing by gravity. this then gave me the 11.5 lbm i drew a box around. if you eliminate gravity from my original calculations you get:
- Bouyant Force = (62.1 lbs/cubic foot) * (.3789 cubic feet) = 23.53 lbs
and Weight = (32 lbs/cubic foot) * (.3789 cubic feet) = 12.12 lbs
Required Force = Bouyant Force - Weight = 11.4 lbs
feel better?