How many bricks can be loaded on a three-ton machine so that the pressure exerted by the machine

| July 1, 2021 | education

How many bricks can be loaded on a three-ton machine so that the pressure exerted by the machine on the ground is 10 MPa? The contact area of the wheels with the ground is 120 cm2. The volume of one brick is considered equal to 2 dm3, and its density is 1500 kg / m3?

Given: P – ground pressure (P = 10 * 10 ^ 6 Pa); S – the area of contact of the wheels with the ground (S = 120 * 10 ^ -4 m2); g – acceleration due to gravity (g ≈ 9.8 m / s2); mm – machine weight (mm = 3 * 10 ^ 3 kg); ρк – brick density (ρк = 1500 kg / m3); V is the volume of one brick (V = 2 dm3 = 2 * 10 ^ -3 m3).

Formula: P = F / S = m * g / S = (mm + mk) * g / S = (mm + n * ρk * V) * g / S and n = (P * S / g – mm) / (ρк * V).

Calculation: n = (10 * 10 ^ 6 * 120 * 10 ^ -4 / 9.8 – 3 * 10 ^ 3) / (1500 * 2 * 10 ^ -3) = 3082 bricks.



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