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).

1 answer

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.