Question

Найти центростремительное ускорение точек колеса автомобиля, соприкасающихся с дорогой, если автомобиль движется со скоростью 72 км/ч, а колесо вращается с частотой 8 Гц

Answer 1

V=72 км/ч=20 м/с
v=2πγR
R=v/2πγ
а ц/с=v²/R=v²:v/2πγ=2πγv=6,28*8*20=1004,8 м/с²

Answer 2

Finding the Centripetal Acceleration of Points on a Car Wheel in Contact with the Road

To find the centripetal acceleration of points on a car wheel in contact with the road, we need to use the formula for centripetal acceleration:

Centripetal Acceleration (a) = (v^2) / r

Where: - v is the linear velocity of the car - r is the radius of the wheel

In this case, we are given that the car is moving with a speed of 72 km/h and the wheel is rotating at a frequency of 8 Hz.

Let's convert the given values to the appropriate units before calculating the centripetal acceleration.

1. Convert the car's speed from km/h to m/s: - 1 km/h = 0.2778 m/s - Therefore, the car's speed is 72 km/h * 0.2778 m/s = 20 m/s.

2. Calculate the linear velocity of a point on the wheel: - The linear velocity of a point on the wheel is equal to the circumference of the wheel multiplied by the frequency of rotation. - The formula for the circumference of a circle is C = 2πr, where r is the radius of the wheel. - Since the frequency of rotation is given as 8 Hz, the time period (T) is 1/8 seconds. - Therefore, the linear velocity (v) of a point on the wheel is v = (2πr) / T. - Substituting the given values, we have v = (2πr) / (1/8) = 16πr m/s.

Now, we can equate the linear velocity of the car to the linear velocity of a point on the wheel and solve for the radius (r) of the wheel.

3. Equate the linear velocities: - The linear velocity of the car is 20 m/s, and the linear velocity of a point on the wheel is 16πr m/s. - Therefore, 20 m/s = 16πr m/s. - Solving for r, we have r = (20 m/s) / (16π) = 1.26 m.

Now that we have the radius of the wheel, we can calculate the centripetal acceleration of points on the wheel in contact with the road.

4. Calculate the centripetal acceleration: - Using the formula for centripetal acceleration, a = (v^2) / r, where v is the linear velocity and r is the radius of the wheel. - Substituting the given values, we have a = (20 m/s)^2 / 1.26 m = 317.46 m/s^2.

Therefore, the centripetal acceleration of points on the car wheel in contact with the road is approximately 317.46 m/s^2.

Please note that this calculation assumes that the car is moving in a straight line and that the points on the wheel in contact with the road are not slipping or sliding.

Let me know if there's anything else I can help you with!