Calculate the lifting force (weight of the load in kilograms), for a raft consisting of 10 pine logs, if the length of each log

| June 17, 2021 | education

Calculate the lifting force (weight of the load in kilograms), for a raft consisting of 10 pine logs, if the length of each log is 4 meters, its diameter is 25 cm, the density of the tree (pine) is 0.52 g / cm3.

Р = Fa – Fт.
P – max. weight (P = m * g, m – max. weight of the load, g – gravitational acceleration (g = 10 m / s²)).
Fa is the strength of Archimedes; Fa = ρw * g * V, ρw is the density of water (ρ = 1000 kg / m ^ 3), V is the volume of the raft (V = 10 * (1/4 * ΠD² * h), D = 0.25 m, h = 4 m).
Ft is the force of gravity; Fт = m * g, m – mass of the raft (m = ρс * V, ρс – pine density (ρс = 520 kg / m³)).
m * g = ρв * g * V – ρс * V * g = g * 10 * (1/4 * ΠD² * h) * (ρв – ρс).
m = 10 * (1/4 * ΠD² * h) * (ρв – ρс) = 10 * 0.25 * 3.14 * 0.25² * 4 * (1000 – 520) = 942 kg.
Answer: The lifting force is 942 kg.



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