Question

Шофёр выключил двигатель автомобиля при скорости 72 км/ч. Через 3.4с автомобиль остановился. Сила трения колёс по асфальту равна 5880Н. Чему был равен импульс автомобиля в момент выключения двигателя? Какова масса автомобиля?

Answer 1

P=Ft=5880*3,4=19992 Н*с
m=p/V=19992/20=999,6 кг

Answer 2

Impulse of the Car at the Moment of Engine Shutdown

To calculate the impulse of the car at the moment of engine shutdown, we can use the principle of conservation of momentum. The impulse is equal to the change in momentum of the car.

The momentum of an object is defined as the product of its mass and velocity. In this case, the momentum of the car before the engine shutdown is equal to the product of its mass and velocity.

Given: - Speed of the car before engine shutdown: 72 km/h - Time taken for the car to stop: 3.4 s - Frictional force between the wheels and the asphalt: 5880 N

To calculate the impulse, we need to convert the speed from km/h to m/s. We can use the formula:

Impulse = Change in momentum = Final momentum - Initial momentum

Calculating the Initial Momentum

The initial momentum of the car can be calculated using the formula:

Initial momentum = mass × initial velocity

Since the car is moving at a constant speed before the engine shutdown, the initial velocity is equal to the speed of the car, which is 72 km/h. Converting this to m/s:

Initial velocity = 72 km/h × (1000 m/1 km) × (1 h/3600 s) = 20 m/s

Now, we need to find the mass of the car to calculate the initial momentum.

Calculating the Mass of the Car

To calculate the mass of the car, we can use the formula:

Force = mass × acceleration

In this case, the force is the frictional force between the wheels and the asphalt, which is given as 5880 N. The acceleration can be calculated using the formula:

Acceleration = Change in velocity / Time taken

The change in velocity is equal to the initial velocity, as the car comes to a stop. The time taken is given as 3.4 s.

Substituting the values into the formula:

Acceleration = 20 m/s / 3.4 s = 5.88 m/s^2

Now, we can calculate the mass of the car:

Mass = Force / Acceleration = 5880 N / 5.88 m/s^2 = 1000 kg

Therefore, the mass of the car is 1000 kg.

Calculating the Final Momentum

The final momentum of the car is equal to the product of its mass and final velocity. Since the car comes to a stop, the final velocity is 0 m/s.

Final momentum = mass × final velocity = 1000 kg × 0 m/s = 0 kg·m/s

Calculating the Impulse

Now, we can calculate the impulse of the car at the moment of engine shutdown using the formula:

Impulse = Final momentum - Initial momentum = 0 kg·m/s - (1000 kg × 20 m/s) = -20,000 kg·m/s

Therefore, the impulse of the car at the moment of engine shutdown is -20,000 kg·m/s.

Please note that the negative sign indicates that the direction of the impulse is opposite to the initial momentum of the car.