If 182 lbs of force keeps a 1500 lb car from skidding on a curve of radius 600 ft at 35 mph, what force would keep the same car from skidding on a curve of radius 750 ft at 50 mph
To solve this problem, we can use the concept of centripetal force. Centripetal force is the force required to keep an object moving in a circular path. 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
r is the radius of the curve
In this case, we are given the mass of the car, but we do not need it to find the centripetal force since it cancels out in the formula.
First, let's convert the given units to a consistent system. We'll convert the radius from feet to miles and the velocity from miles per hour to feet per second.
R1 = 600 ft = 600 ft * 1 mile / 5280 ft = 0.1136 miles
V1 = 35 mph = 35 mph * 5280 ft / 3600 s ≈ 51.33 ft/s
Now we can calculate the centripetal force for the first scenario:
F1 = (m * V1^2) / R1
= V1^2 / R1
= 51.33^2 / 0.1136
≈ 23138 ft-lbs
Now let's find the force required for the second scenario.
R2 = 750 ft = 750 ft * 1 mile / 5280 ft = 0.1420 miles
V2 = 50 mph = 50 mph * 5280 ft / 3600 s ≈ 73.33 ft/s
F2 = V2^2 / R2
= 73.33^2 / 0.1420
≈ 38061 ft-lbs
Therefore, the force required to keep the same car from skidding on a curve of radius 750 ft at 50 mph is approximately 38,061 ft-lbs.