In: Physics
Three children, each of weight 361 N, make a log raft by lashing together logs of diameter 0.21 m and length 1.60 m. How many logs will be needed to keep them afloat in fresh water? Take the density of the logs to be 800 kg/m3.
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Three children, each of weight 356 N, make a log raft by lashing together logs of diameter 0.30m and length 1.80 m. How many logs will be needed to keep them afloat in fresh water? Take the density of logs to be 800 kg/m^3.
The buoyancy created by each log can be found by thedifference
between the weight of a log and the weight of the samevolume of
water... like this:
.
volume of a log = area * length = pi*r^2 L = pi * 0.15^2 * 1.80 =
0.127235 m3
.
mass of a log = density * volume = 800 *0.127235 = 101.79 kg
.
mass of same volume of water = 1000 *0.127235 = 127.235 kg
.
difference in mass = 127.235 - 101.79 = 25.447 kg
.
difference in weight = mg = 25.447 * 9.80 = 249.38 Newtons
.
Each log can support 249.38 N of weight. Thekids weigh 356 * 3 =
1068 N
.
So they need 1068 / 249.38 = 4.28 logs... but they cant have
afraction
5 logs