Question

Помогите пожалуйста С какой силой должен тормозить автомобиль массой 700 кг, чтобы его тормозной путь на дороге, наклоненной под углом 25° к горизонту, составил 30 м? Начальная скорость автомобиля вверх по дороге 60 км/ч.​

Answer 1

Ответ:

V = 60 км/ч = 60000/3600 = 50/3 = 16,7 м/с.

Исходная (кинетическая) энергия 0,5*mV^2 равна работе силы сопротивления F на пути S и работе подъема на высоту h = S*sin25°:

mV^2/2 = F*S + mgh = F*S + mg*(S*sin25°) ==>

F = (mV^2/2 – mg*(S*sin25°))/S = 700*((50/3)^2/2 – 9.8*30*sin(25))/30 = 341.6 H.

ОТВЕТ: F = ~ 342 Н

Answer 2

Calculation of the Braking Force

To calculate the braking force required to stop a car, we need to consider the gravitational force acting on the car due to the incline of the road and the frictional force between the tires and the road surface.

The gravitational force acting on the car can be calculated using the formula:

F_gravity = m * g * sin(θ)

Where: - F_gravity is the gravitational force - m is the mass of the car (700 kg in this case) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of the incline (25° in this case)

The frictional force can be calculated using the formula:

F_friction = μ * m * g * cos(θ)

Where: - F_friction is the frictional force - μ is the coefficient of friction between the tires and the road surface (assumed to be 0.7) - m is the mass of the car (700 kg) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of the incline (25°)

The total braking force required to stop the car can be calculated by adding the gravitational force and the frictional force:

F_braking = F_gravity + F_friction

Let's calculate the values:

F_gravity = 700 kg * 9.8 m/s^2 * sin(25°) F_friction = 0.7 * 700 kg * 9.8 m/s^2 * cos(25°) F_braking = F_gravity + F_friction

Calculating the values using the given formula:

F_gravity ≈ 3037.9 N F_friction ≈ 4707.3 N F_braking ≈ 7745.2 N

Therefore, the braking force required to stop the car is approximately 7745.2 Newtons.

Please note that the above calculations assume ideal conditions and do not take into account factors such as air resistance, tire conditions, and other variables that may affect the actual braking force required.