Question

Автомобиль массой 1 т проходит середину выпуклого моста со скоростью 72 км/ч . Найти вес автомобиля если радиус моста равен 100м .(ответ дать в кН)

Answer 1

Problem Analysis

We are given the following information: - The mass of the car is 1 ton (1000 kg). - The car is passing through the center of a convex bridge with a radius of 100 m. - The car's speed is 72 km/h.

We need to find the weight of the car in kilonewtons (kN).

Solution

To solve this problem, we can use the centripetal force formula:

F = m * v^2 / r

Where: - F is the centripetal force - m is the mass of the car - v is the velocity of the car - r is the radius of the bridge

To find the weight of the car, we need to convert the mass from kilograms to newtons using the formula:

Weight = mass * g

Where: - Weight is the force due to gravity acting on the car - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Finally, we can convert the weight from newtons to kilonewtons by dividing by 1000.

Let's calculate the weight of the car step by step.

Calculations

Given: - Mass of the car (m) = 1000 kg - Velocity of the car (v) = 72 km/h = 20 m/s - Radius of the bridge (r) = 100 m - Acceleration due to gravity (g) = 9.8 m/s^2

1. Calculate the centripetal force (F): - F = m * v^2 / r - F = 1000 kg * (20 m/s)^2 / 100 m - F = 40000 N

2. Calculate the weight of the car (Weight): - Weight = m * g - Weight = 1000 kg * 9.8 m/s^2 - Weight = 9800 N

3. Convert the weight to kilonewtons: - Weight in kN = Weight / 1000 - Weight in kN = 9800 N / 1000 - Weight in kN = 9.8 kN

Answer

The weight of the car is 9.8 kN.