A car with a mass of 2 tons, passing along a concave bridge with a radius of 50 m, has a weight of 45 kN.

A car with a mass of 2 tons, passing along a concave bridge with a radius of 50 m, has a weight of 45 kN. How fast is the car moving?

The y-axis is upward.

The car is affected by:

– the reaction force of the bridge is equal to the weight of the car P – is directed upwards.

– gravity Fт = mg – directed downward.

The car moves with centripetal acceleration a = V² / R.

Acceleration a is directed to the center of the circle – up.

Newton’s second law projected onto the Y-axis:

ma = P – mg.

m V² / R = P – mg.

V = √ (R * (P – mg) / m) = √ (R * (P / m – g)) = √ (50 m * (45,000 N / 2000 kg – 10 m / s²)) = √ ( 625 m² / s²) = 25 m / s;

V = 25 m / s = 25 m / s * 3600 s / h = 90,000 m / h = 90 km / h.

Answer: 25 m / s (90 km / h).