At a Grand Prix, drivers sustain lateral accelerations (sideways) about five times the acceleration due to gravity while driving around curves at speeds of 288 km/h. Assuming a circular curve, find the radius of that section of the track.
To find the radius of the section of the track, we can use the formula for centripetal acceleration:
ac = (v^2) / r
Where:
ac = centripetal acceleration
v = speed of the car
r = radius of the curve
First, let's convert the speed from km/h to m/s:
v = 288 km/h = (288 * 1000) / 3600 = 80 m/s
Now, we have the given acceleration in terms of g, which is the acceleration due to gravity:
ac = 5 g
We know that g is approximately 9.8 m/s^2. Substituting this value, the equation becomes:
5 g = (v^2) / r
Rearranging the equation, we can solve for r:
r = (v^2) / (5 g)
Substituting the given values:
r = (80^2) / (5 * 9.8) = 12800 / 49 ≈ 261.22 meters
Therefore, the radius of that section of the track is approximately 261.22 meters.