Computer-controlled display screens provide drivers in the Indianapolis 500 with a variety of information about how their cars are performing. For instance, as a car is going through a turn, a speed of 87.5 m/s and centripetal acceleration of 2.48 g (2.48 times the acceleration due to gravity) are displayed. Determine the radius of the turn (in meters).
Ac = v^2/R
2.48 * 9.81 = (87.5)^2/R
To determine the radius of the turn, we can use the following equation:
Centripetal acceleration = (v^2) / r
where:
- Centripetal acceleration is given as 2.48 g (2.48 times the acceleration due to gravity)
- Velocity (v) is given as 87.5 m/s
- r is the radius of the turn that we need to find.
Rearranging the equation, we have:
r = (v^2) / Centripetal acceleration
Substituting the given values, we get:
r = (87.5 m/s)^2 / (2.48 * 9.8 m/s^2)
Calculating the equation results in:
r = 3038.28125 / 24.264
r ≈ 125.23 meters
Therefore, the radius of the turn is approximately 125.23 meters.