Determine the mass of a car that, while passing at a speed of 72 km / h, the top of a curved bridge

| July 3, 2021 | education

Determine the mass of a car that, while passing at a speed of 72 km / h, the top of a curved bridge with a radius of curvature of 100 m has a weight of 18 kN.

To find out the mass of the specified car, consider the equality (we take into account that the bridge is concave): m * ac = N – m * g; m * V ^ 2 / r = P – m * g; P = m * V ^ 2 / r + m * g = m * (V ^ 2 / r + g), whence we express: m = P / (V ^ 2 / r + g).

Const: g – acceleration due to gravity (g ≈ 9.81 m / s2).

Data: P – weight at the top (P = 18 kN = 18 * 10 ^ 3 N); V – constant speed (V = 72 km / h, in the SI system V = 20 m / s); r is the radius of the concave bridge (r = 100 m).

Let’s perform the calculation: m = P / (V ^ 2 / r + g) = 18 * 10 ^ 3 / (202/100 + 9.81) ≈ 1303.4 kg.

Answer: The weight of the specified vehicle must be 1303.4 kg.



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