Question

Найти максимальную скорость, с которой вагон массой 60 т может двигаться по кругу радиусом 300 м, если горизонтальная составляющая силы, действующей на рельсы, не должна превышать 80 кН

Answer 1

Воспользуемся уравнением центробежной силы:
mU^2/R = 80000;
U = sqrt(80000R/m) = 20 м/с

Answer 2

Calculating Maximum Speed of the Wagon

To calculate the maximum speed at which a wagon with a mass of 60 tons can move around a circle with a radius of 300 m, given that the horizontal component of the force acting on the rails must not exceed 80 kN, we can use the following steps:

1. Determine the Maximum Horizontal Force: - The maximum horizontal force can be calculated using the formula: \[ F_{\text{max}} = \mu \times N \] where \( \mu \) is the coefficient of friction and \( N \) is the normal force.

2. Calculate the Normal Force: - The normal force can be calculated using the formula: \[ N = m \times g \] where \( m \) is the mass of the wagon and \( g \) is the acceleration due to gravity.

3. Find the Coefficient of Friction: - The coefficient of friction can be determined based on the given conditions and the type of surfaces involved.

4. Calculate the Maximum Speed: - Once the maximum horizontal force is determined, the maximum speed can be calculated using the centripetal force formula: \[ F_{\text{max}} = \frac{m \times v^2}{r} \] where \( m \) is the mass of the wagon, \( v \) is the velocity, and \( r \) is the radius of the circle.

Let's proceed with the calculations based on the given information.

Calculations

1. Determine the Maximum Horizontal Force: - The maximum horizontal force can be calculated using the formula: \[ F_{\text{max}} = \mu \times N \] From Source the value of \( \mu \) is not provided, so we'll proceed to calculate the normal force.

2. Calculate the Normal Force: - The normal force can be calculated using the formula: \[ N = m \times g \] Given: - Mass of the wagon, \( m = 60 \, \text{tons} = 60000 \, \text{kg} \) - Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \) Therefore: \[ N = 60000 \times 9.81 = 588600 \, \text{N} \]

3. Find the Coefficient of Friction: - The coefficient of friction is not provided in the search results. Without this information, we cannot proceed with the calculation of the maximum horizontal force and, subsequently, the maximum speed.

Conclusion

Unfortunately, without the coefficient of friction, we are unable to calculate the maximum speed of the wagon as requested. If you have the coefficient of friction available, please provide it, and I'd be happy to assist further with the calculations.