A 3670 lb car going around an unbanked curve at a constant speed of 25 mph begins to slide (ìs=0.55 and ìk=0.45). What is the radius of the curve?
The static coefficient of friction, which you call ìs=0.55, is the one to use.
Equate the centripetal force to the friction force, and solve for R. The mass of the car will cancel out.
0.55 g = V^2/R
Solve for R.
25 mph = 36.67 ft/s
g = 32.2 ft/s^2
thanks a lot
To find the radius of the curve, we'll start by calculating the centripetal force required to keep the car moving in a circle.
The centripetal force is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the car
v is the velocity
r is the radius of the curve
Given:
m = 3670 lb (mass of the car)
v = 25 mph (velocity)
First, let's convert the mass of the car from pounds (lb) to kilograms (kg).
1 lb is approximately 0.453592 kg. So,
m = 3670 lb * 0.453592 kg/lb
m ≈ 1663.18 kg
Now, let's convert the velocity from mph to m/s.
1 mph is approximately 0.44704 m/s. So,
v = 25 mph * 0.44704 m/s
v ≈ 11.176 m/s
Now, let's substitute the values into the equation for centripetal force:
F = (1663.18 kg * (11.176 m/s)^2) / r
Next, we'll determine the force of static friction (fs) and the maximum force of kinetic friction (fk) using the coefficients of friction provided.
fs = ìs * (m * g)
fk = ìk * (m * g)
Where:
ìs is the coefficient of static friction
ìk is the coefficient of kinetic friction
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Given:
ìs = 0.55
ìk = 0.45
fs = 0.55 * (1663.18 kg * 9.8 m/s^2)
fs ≈ 9045.54 N
fk = 0.45 * (1663.18 kg * 9.8 m/s^2)
fk ≈ 7371.02 N
Since the car is sliding, the maximum force of friction is equal to the force of kinetic friction:
fk = F
Therefore,
7371.02 N = (1663.18 kg * (11.176 m/s)^2) / r
Now, we can solve for the radius (r):
r = (1663.18 kg * (11.176 m/s)^2) / 7371.02 N
Calculating this value will give us the radius of the curve.