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 92.4 m/s and centripetal acceleration of 4.74g (4.74 times the acceleration due to gravity) are displayed. Determine the radius of the turn (in meters).
To determine the radius of the turn, we can use the formula for centripetal acceleration:
a = v^2 / r
Where:
a is the centripetal acceleration,
v is the velocity of the car, and
r is the radius of the turn.
We are given:
v = 92.4 m/s,
a = 4.74g.
First, we need to convert the centripetal acceleration from g to m/s^2. 1 g is equal to 9.8 m/s^2. So,
a = 4.74 * 9.8 m/s^2 = 46.452 m/s^2
Substituting the given values into the formula, we have:
46.452 = (92.4)^2 / r
Rearranging the equation to solve for r, we have:
r = (92.4)^2 / 46.452
Calculating this, we get:
r = 184.23 meters
Therefore, the radius of the turn is 184.23 meters.