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 201 mi/h (89.847 m/s) and a centripetal acceleration of 4.00g (four times the acceleration due to gravity) are displayed. Determine the radius of the turn (in meters).
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To determine the radius of the turn, we can start by using the formula for centripetal acceleration:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity
r = radius
Given that the speed (v) is 89.847 m/s and the centripetal acceleration (a) is 4.00g, which is 4 times the acceleration due to gravity (4 * 9.8 m/s^2), we can plug in the values into the formula:
4 * 9.8 m/s^2 = (89.847 m/s)^2 / r
Solving for r:
4 * 9.8 m/s^2 = 89.847^2 m^2/s^2 / r
39.2 m/s^2 = 8072.75 m^2/s^2 / r
39.2 m/s^2 * r = 8072.75 m^2/s^2
r = 8072.75 m^2/s^2 / 39.2 m/s^2
r ≈ 206.12 meters
Therefore, the radius of the turn is approximately 206.12 meters.
To determine the radius of the turn, we can use the formula for centripetal acceleration:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity of the car
r = radius of the turn
We are given:
v = 89.847 m/s
a = 4.00g = 4.00 * 9.8 m/s^2 (since acceleration due to gravity is approximately 9.8 m/s^2)
Plugging in these values into the formula, we have:
4.00 * 9.8 = (89.847)^2 / r
Simplifying this equation:
r = (89.847)^2 / (4.00 * 9.8)
Using a calculator:
r ≈ 70.505 meters
Therefore, the radius of the turn is approximately 70.505 meters.
a=v²/r
a=4*9.81 m/s²
v=89.847 m/s
solve for r