Final answer:
To keep the car from sliding off the road, a minimum coefficient of static friction of 0.54 is needed.
Step-by-step explanation:
To find the minimum coefficient of static friction needed to keep the car from sliding off the road, we can use the equation:
Fc = m × v2 / r
Where:
- Fc is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- r is the radius of the circular track
Plugging in the values given, we have:
Fc = (1300 kg) × (22 m/s)2 / (85 m)
= 6,724 N
Next, we can calculate the maximum static friction force using the equation:
fs = μs × N
Where:
- fs is the static friction force
- μs is the coefficient of static friction
- N is the normal force
The normal force can be found as:
N = m × g
Where g is the acceleration due to gravity.
The maximum static friction force would occur when the car is on the verge of sliding off the road, meaning fs = Fc. Therefore:
Fc = μs × N
Substituting the known values, we get:
6,724 N = μs × (1300 kg × 9.8 m/s2)
Solving for μs, we find:
μs = 0.54
Therefore, a minimum coefficient of static friction of 0.54 is needed to keep the car from sliding off the road.