If 182 lbs of force keeps a 1500 lb car from skidding on a curve of radius 500 ft at 30 mph, what force would keep the same car from skidding on a curve of radius 800 ft at 45 mph
To determine the force required to keep a car from skidding on a curve, we can use the concept of centripetal force. Centripetal force is the force exerted on an object moving in a circular path, directed towards the center of the circle.
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F is the centripetal force,
m is the mass of the object,
v is the velocity of the object, and
r is the radius of the circular path.
In this case, we need to find the force required to keep the car from skidding on a curve with a radius of 800 ft at 45 mph.
Step 1: Convert the speed from mph to ft/s
To use the formula, we need to convert the velocity from miles per hour (mph) to feet per second (ft/s).
1 mph = 1.467 ft/s
So, 45 mph = 45 * 1.467 ft/s = 66.165 ft/s (rounded to three decimal places).
Step 2: Calculate the centripetal force
Using the formula F = (m * v^2) / r, we can plug in the values we have:
F = (1500 lb * (66.165 ft/s)^2) / 800 ft
Step 3: Solve for the centripetal force
Calculating the equation, we have:
F = (1500 lb * 4369.881225 ft^2/s^2) / 800 ft
F = 6554821.8375 lb ft/s^2
Therefore, the force required to keep the car from skidding on a curve with a radius of 800 ft at 45 mph is approximately 6,554,822 lb ft/s^2.