The car weighing 5t moves with a constant modulo by a speed of 36 km / h along the convex bridge

The car weighing 5t moves with a constant modulo by a speed of 36 km / h along the convex bridge with a radius of 100 m. Determine the weight of the car at the upper point of the bridge.

M = 5 T = 5000 kg.

G = 10 m / s2.

V = 36 km / h = 10 m / s.

R = 100 m.

R – ?

The weight of the car is called the power with which the car presses on the bridge.

Consider what forces act on the car. It operates 2 forces: the strength of gravity FT, directed vertically down, the power of the pressure of the bridge on the car directed vertically upwards.

M * A = FT + N – 2 Newton’s law in vector form.

The centripetal acceleration A directed along the radius of the curvature of the bridge to the center, that is, vertically down and is determined by the formula: a = V ^ 2 / R.

For the projections for the vertical axis 2, Newton’s law will take the form: – M * A = – FT + N.

N = FT – M * a.

The force of gravity FT is determined by the formula: FT = M * G.

N = M * G – M * A = M * (G – a) = M * (G – V ^ 2 / R).

According to the 3 Newton law, the force of N is equal to the strength of opposition p: N = R.

P = M * (G – V ^ 2 / R).

P = 5000 kg * (10 m / s2 – (10 m / s) ^ 2/100 m) = 45000 N.

Answer: At the upper point of the convex bridge, the weight of the car is p = 45000 N. m = 5 T = 5000 kg.

G = 10 m / s2.

V = 36 km / h = 10 m / s.

R = 100 m.

R – ?

The weight of the car is called the power with which the car presses on the bridge.

Consider what forces act on the car. It operates 2 forces: the strength of gravity FT, directed vertically down, the power of the pressure of the bridge on the car directed vertically upwards.

M * A = FT + N – 2 Newton’s law in vector form.

Centripetal acceleration A directed along the radius of the curvature of the bridge to the center, that is, vertically down and is determined by the formula: A = V2 / R.

For the projections for the vertical axis 2, Newton’s law will take the form: – M * A = – FT + N.

N = FT – M * a.

The force of gravity FT is determined by the formula: FT = M * G.

N = M * G – M * A = M * (G – a) = M * (G – V ^ 2 / R).

According to the 3 Newton law, the force of N is equal to the strength of opposition p: N = R.

P = M * (G – V ^ 2 / R).

P = 5000 kg * (10 m / s2 – (10 m / s) ^ 2/100 m) = 45000 N.

Answer: At the top point of the convex bridge, the weight of the car is p = 45000 N.

M = 5 T = 5000 kg.

G = 10 m / s2.

V = 36 km / h = 10 m / s.

R = 100 m.

R – ?

The weight of the car is called the power with which the car presses on the bridge.

Consider what forces act on the car. It operates 2 forces: the strength of gravity FT, directed vertically down, the power of the pressure of the bridge on the car directed vertically upwards.

M * A = FT + N – 2 Newton’s law in vector form.

The centripetal acceleration A directed along the radius of the curvature of the bridge to the center, that is, vertically down and is determined by the formula: a = V ^ 2 / R.

For the projections for the vertical axis 2, Newton’s law will take the form: – M * A = – FT + N.

N = FT – M * a.

The force of gravity FT is determined by the formula: FT = M * G.

N = M * G – M * A = M * (G – a) = M * (G – V ^ 2 / R).

According to the 3 Newton law, the force of N is equal to the strength of opposition p: N = R.

P = M * (G – V ^ 2 / R).

P = 5000 kg * (10 m / s2 – (10 m / s) ^ 2/100 m) = 45000 N.

Answer: At the upper point of the convex bridge, the weight of the car is p = 45000 N. m = 5 T = 5000 kg.

G = 10 m / s2.

V = 36 km / h = 10 m / s.

R = 100 m.

R – ?

The weight of the car is called the power with which the car presses on the bridge.

Consider what forces act on the car. It operates 2 forces: the strength of gravity FT, directed vertically down, the power of the pressure of the bridge on the car directed vertically upwards.

M * A = FT + N – 2 Newton’s law in vector form.

Centripetal acceleration A directed along the radius of the curvature of the bridge to the center, that is, vertically down and is determined by the formula: A = V2 / R.

For the projections for the vertical axis 2, Newton’s law will take the form: – M * A = – FT + N.

N = FT – M * a.

The force of gravity FT is determined by the formula: FT = M * G.

N = M * G – M * A = M * (G – a) = M * (G – V ^ 2 / R).

According to the 3 Newton law, the force of N is equal to the strength of opposition p: N = R.

P = M * (G – V ^ 2 / R).

P = 5000 kg * (10 m / s2 – (10 m / s) ^ 2/100 m) = 45000 N.

Answer: At the top point of the convex bridge, the weight of the car is p = 45000 N.