At what speed a car weighing 800 kg must pass the middle of the concave bridge to be weightless. The radius of curvature is 40m.

P = 0 N.
m = 800 kg.
g = 10 m / s2.
R = 40 m.
V -?
A state of weightlessness is a state in which the weight of the body is 0. That is, when passing the middle of the curved bridge, the car should not act on the bridge with a force: P = 0.
Two forces act on the car: the force of gravity Ft directed vertically downward, the force N of the axle pressure directed vertically upward.
m * a = Fт + N – 2 Newton’s law in vector form.
For projections onto the vertical axis 2, Newton’s law will take the form: – m * a = – Fт + N.
N = Fт – m * a.
The force of gravity Ft is determined by the formula: Ft = m * g.
N = m * g – m * a.
The centripetal acceleration a is expressed by the formula: a = V ^ 2 / R.
N = m * g – m * V ^ 2 / R.
According to Newton’s 3 laws, the force N with which the bridge presses on the car is equal to the force with which the car presses on the bridge Р: N = P.
P = m * g – m * V ^ 2 / R = 0.
m * g = m * V2 / R.
V = √ (g * R).
V = √ (10 m / s2 * 40 m) = 20 m / s.
Answer: the car must travel across the bridge at a speed of V = 20 m / s.