is the roadway flat?
if so,
mv^2/r-mg*coeff=0
solve for coeff
if so,
mv^2/r-mg*coeff=0
solve for coeff
Select one:
a. 73°
b. 67°
c. 75°
d. 69°
e. 71°
In this case, the centripetal force is provided by the friction between the car's tires and the road. The equation for centripetal force is:
F = m * a
Where:
F is the centripetal force
m is the mass of the car
a is the centripetal acceleration
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
Where:
v is the velocity of the car
r is the radius of the curve
In this case, the velocity of the car is 16 m/s and the radius of the curve is 100 m. Plugging these values into the equation, we get:
a = (16 m/s)^2 / 100 m
a = 2.56 m/s^2
Now we need to calculate the centripetal force using the formula F = m * a. However, we don't know the mass of the car.
To continue, we need the weight of the car. Let's assume the weight is W. The normal force acting on the car, which is equal to the weight, is given by:
N = W = m * g
Where:
g is the acceleration due to gravity
Assuming a typical value for the acceleration due to gravity of 9.8 m/s^2, we can substitute the weight equation into the centripetal force equation:
F = (m * g) * a
Since we know the centripetal force is provided by the friction between the tires and the road, and the maximum frictional force is given by the product of the coefficient of friction (μ) and the normal force (N), we can write:
F = μ * N
Substituting N = m * g into the equation, we get:
F = μ * (m * g)
Now we have two expressions for the centripetal force: F = (m * g) * a and F = μ * (m * g). Setting them equal, we have:
(m * g) * a = μ * (m * g)
Canceling out the mass and acceleration due to gravity terms:
a = μ * g
Solving for the coefficient of friction μ:
μ = a / g
Plugging in the values of a and g:
μ = 2.56 m/s^2 / 9.8 m/s^2
μ ≈ 0.26
Therefore, the coefficient of friction between the car's tires and the road must be approximately 0.26 for the car to safely negotiate the curve at the posted speed of 35 mph (approximately 16 m/s).