Question

Автомобиль массой m=5 т движется с постоянной скоростью v=10 м/с а) по выпуклому мосту б) по вогнутому мосту. С какой силой нормального давления действует автомобиль на мост в его средней части? Радиус кривизны моста R=50 м.

Answer 1

Ответ: 40кН; 60кН

Объяснение:

Дано:

m=5т=5000кг

V=10м/с

R=50м

========

Р1-?; Р2-?

Р1=m(g-V²/R)=5000*(10-10²/50)=40000Н=40кН

Р2=m(g+V²/R)=5000*(10+10²/50)=60000Н=60кН

Answer 2

Calculation of the Normal Force on the Car

To calculate the normal force exerted by the car on the bridge, we need to consider the forces acting on the car in both scenarios: when it is moving on a convex bridge and when it is moving on a concave bridge.

Let's start with the scenario where the car is moving on a convex bridge.

Convex Bridge Scenario

In this scenario, the car is moving on a convex bridge with a radius of curvature (R) equal to 50 meters. The car has a mass (m) of 5 tons and is moving with a constant velocity (v) of 10 m/s.

To calculate the normal force (N) exerted by the car on the bridge in its middle part, we need to consider the forces acting on the car. These forces include the gravitational force (mg) and the centripetal force (Fc) required to keep the car moving in a circular path.

The gravitational force (mg) is given by the product of the mass (m) and the acceleration due to gravity (g). Since the car is not accelerating vertically, the gravitational force is balanced by the normal force (N) exerted by the bridge on the car.

The centripetal force (Fc) required to keep the car moving in a circular path is given by the equation Fc = (mv^2) / R, where m is the mass of the car, v is its velocity, and R is the radius of curvature of the bridge.

Since the car is moving with a constant velocity, the net force acting on the car in the vertical direction is zero. Therefore, the normal force (N) exerted by the bridge on the car is equal to the gravitational force (mg) plus the centripetal force (Fc).

Let's calculate the normal force (N) in the middle part of the bridge:

Gravitational force (mg) = 5 tons * 9.8 m/s^2 = 49,000 NCentripetal force (Fc) = (5 tons * (10 m/s)^2) / 50 m = 1,000 N Normal force (N) = Gravitational force (mg) + Centripetal force (Fc) = 49,000 N + 1,000 N = 50,000 N

Therefore, the normal force exerted by the car on the bridge in its middle part when moving on a convex bridge is 50,000 N.

Concave Bridge Scenario

In the scenario where the car is moving on a concave bridge, the calculation of the normal force is similar to the convex bridge scenario. The only difference is that the direction of the centripetal force changes.

The normal force (N) exerted by the bridge on the car is still equal to the gravitational force (mg) plus the centripetal force (Fc). However, in this case, the centripetal force (Fc) is directed towards the center of the circular path, which is opposite to the gravitational force.

The magnitude of the centripetal force (Fc) remains the same as in the convex bridge scenario, but its direction is reversed.

Therefore, the normal force exerted by the car on the bridge in its middle part when moving on a concave bridge is also 50,000 N.

Summary

In summary, when the car is moving on both a convex and a concave bridge with a radius of curvature of 50 meters, the normal force exerted by the car on the bridge in its middle part is 50,000 N in both scenarios.

Please note that the calculations provided are based on the given information and assumptions.