An Indy car with a speed of 120 km/h goes around a level, circular track with a radius of 1 km. What is the centripetal acceleration of the car (in m/s/s)?
a = v²/R,
where
v = 120 km/h = 120000/3600 m/s=33.3 m/s, R = 1000 m
a =1.35•10^7 m/s²
To find the centripetal acceleration of the car, we can use the formula:
Centripetal acceleration = (velocity)^2 / radius
First, let's convert the speed of the car from km/h to m/s. We know that 1 km/h = 0.2778 m/s. Therefore, the speed of the car is:
120 km/h * 0.2778 m/s = 33.33 m/s (approx.)
Now, we can calculate the centripetal acceleration using the formula:
Centripetal acceleration = (33.33 m/s)^2 / 1000 m
Centripetal acceleration = 1111.1 m^2/s^2 / 1000 m
Centripetal acceleration ≈ 1.111 m/s^2
So, the centripetal acceleration of the car is approximately 1.111 m/s^2.
To calculate the centripetal acceleration of the car, we can use the formula:
Centripetal acceleration (a) = (Velocity (v))^2 / Radius (r)
First, we need to convert the velocity from km/h to m/s since the formula requires the velocity to be in meters per second (m/s).
Given: Velocity (v) = 120 km/h, Radius (r) = 1 km
To convert the velocity from km/h to m/s, we need to use the conversion factor 1 km/h = 0.27778 m/s.
So, the velocity in m/s would be:
120 km/h * (0.27778 m/s)/(1 km/h) = 33.3333 m/s
Now, we can plug in the values into the formula:
Centripetal acceleration (a) = (33.3333 m/s)^2 / 1 km
Since the radius is given in kilometers, we need to convert it to meters by multiplying by 1000.
Centripetal acceleration (a) = (33.3333 m/s)^2 / (1 km * 1000 m/km)
Simplifying the equation:
a = (33.3333^2 m^2/s^2) / 1000 m
a = 1111.1089 m^2/s^2 / 1000 m
a = 1.1111 m/s^2
Therefore, the centripetal acceleration of the car is 1.1111 m/s^2.