What is the smallest number of logs with a length of 10 m and a cross-sectional area of 300 cm2 should be taken for a raft in order to transport a car weighing 1000 kg across the river on it?
Given: h (log length) = 10 m; S (cross-sectional area of the log) = 300 cm2 (300 * 10-4 m2); m1 (vehicle weight) = 1000 kg.
Constants: ρс (average density of pine) = 520 kg / m3.
The number of logs for the raft is determined from the equality: Ft1 + Ft2 = Fа.
m1 * g + n * ρс * V * g = n * ρв * g * V.
m1 + n * ρс * h * S = n * ρw * h * S.
1000 + n * 520 * 10 * 300 * 10-4 = n * 1000 * 10 * 300 * 10-4.
1000 = n * 10 * 300 * 10-4 * (1000 – 520).
n = 6.94 ≈ 7 logs.
Answer: For the raft, you need to take 7 logs.
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