When you take your 1700-kg car out for a spin, you go around a corner of radius 55 m with a speed of 20 m/s. The coefficient of static friction between the car and the road is 0.88.Assuming your car doesn't skid, what is the force exerted on it by static friction?
m Ac = m v^2/r
= 1700 * 400 / 55 Newtons
To determine the force exerted on the car by static friction, we can use the centripetal force formula:
F = (m * v^2) / r
where:
F is the centripetal force
m is the mass of the car (1700 kg)
v is the velocity of the car (20 m/s)
r is the radius of the curve (55 m)
Before we calculate the centripetal force, we need to check if the static friction is sufficient to enable the car to go around the curve without skidding.
The maximum static friction force can be calculated using the formula:
F_static_max = μ_s * N
where:
F_static_max is the maximum static friction force
μ_s is the coefficient of static friction (0.88, given in the question)
N is the normal force, which is equal to the weight of the car, given by:
N = m * g
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2)
First, calculate the weight of the car:
Weight = m * g
Weight = 1700 kg * 9.8 m/s^2
Now, calculate the normal force:
N = Weight
N = 16660 N
Next, calculate the maximum static friction force:
F_static_max = μ_s * N
F_static_max = 0.88 * 16660 N
Finally, compare the maximum static friction force to the required centripetal force to determine if the car will skid or not:
If the maximum static friction force is greater than or equal to the required centripetal force, then the car will not skid and the force exerted on it by static friction will be equal to the required centripetal force.
If the maximum static friction force is less than the required centripetal force, then the car will skid and the force exerted on it by static friction will be equal to the maximum static friction force.