A racecar driver has to hold on tightly when going around a banked curve. Approximately what is the centripetal force on a 2,540.0 kg car going around a circle with a diameter of 190.0 meters at 25.0 m/s?
R = 190/2
once again m v^2 / R
To calculate the centripetal force on a car going around a banked curve, we need to use the formula:
F = (m * v^2) / r
where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car, and
r is the radius of the curve.
In this case, the diameter of the circle is given, so we need to convert it to the radius by dividing it by 2:
r = 190.0 m / 2 = 95.0 m
Now we can plug in the values into the formula:
F = (2,540.0 kg * (25.0 m/s)^2) / 95.0 m
First, square the velocity:
v^2 = 25.0 m/s * 25.0 m/s = 625.0 m^2/s^2
Now, substitute the values into the formula:
F = (2,540.0 kg * 625.0 m^2/s^2) / 95.0 m
Simplify the equation:
F = 16,812,500 kg · m/s^2 / 95.0 m
The units cancel out:
F = 176,921 kg · m/s^2
Therefore, the centripetal force on the car is approximately 176,921 kg · m/s^2.