A steel bar in the shape of a rectangular parallelepiped is placed on a flat horizontal surface so that it touches

| September 29, 2021 | education

A steel bar in the shape of a rectangular parallelepiped is placed on a flat horizontal surface so that it touches it with one of its faces. The pressure that the bar exerts on this surface can be p1 = 3000 Pa, p2 = 5200 Pa or p3 = 15600 Pa, depending on which face it lies on. Determine the mass of the bar. Express your answer in kg, rounded to the nearest whole number. Density of steel ρ = 7800 kg / m3. Free fall acceleration g = 10 N / kg.

Task data: P1 = 3000 Pa; P2 = 5200 Pa; P3 = 15,600 Pa; ρ = 7800 kg / m3; g = 10 N / kg.

P1 = F / S1 = m * g / (a * b) = ρ * V * g / (a * b) = ρ * c * g; c = P1 / (ρ * g).

P2 = F / S2 = m * g / (a * c) = ρ * V * g / (a * c) = ρ * b * g; b = P2 / (ρ * g).

P3 = F / S3 = m * g / (b * c) = ρ * V * g / (b * c) = ρ * a * g; a = P3 / (ρ * g).

Bar mass: m = ρ * V = ρ * a * b * c = ρ * (P1 / (ρ * g)) * P2 / (ρ * g) * P3 / (ρ * g) = P1 * P2 * P3 / (ρ ^ 2 * g ^ 3) = 3000 * 5200 * 15600 / (78002 * 103) = 4 kg.



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