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.
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