A flat (unbanked) curve on a highway has a radius of 200 m. A car rounds the curve at a speed of 26.0 m/s.
What is the minimum coefficient of friction that will prevent sliding?
Our professor didn't even go over this, and it is way more complex than anything in the book. Plus, I am a communications major who got stuck. So please HELP!
What is the acceleration going around the curve? a= v^2/radius
Force friction = normal force*mu
That friction force has to equal m*accelerationabove.
Set them equal, where normal force is mg, and solve for mu.
afadf
gkj
k(min)=(V^2/(gr))
so, (26^2/(9.8*200))= .34
To find the minimum coefficient of friction that will prevent sliding on the flat curve, we need to use the equation:
friction force = normal force * coefficient of friction
First, let's find the acceleration of the car going around the curve. The acceleration is given by the formula:
acceleration = velocity^2 / radius
Substituting the given values, we have:
acceleration = (26.0 m/s)^2 / 200 m = 6.76 m/s^2
Next, we can find the normal force acting on the car. The normal force is equal to the weight of the car, which is given by the formula:
normal force = mass * gravity
Since the mass is not given, we can't calculate the exact value of the normal force. However, we can find the minimum coefficient of friction by considering the worst-case scenario, which is when the car is barely not sliding. In this case, the normal force would be equal to the weight of the car, and the friction force would be equal to the maximum friction force that can be provided by the tires.
Setting the friction force equal to the product of the minimum coefficient of friction and the normal force, we have:
minimum coefficient of friction * normal force = mass * acceleration
Since the mass can cancel out from both sides of the equation, we can rewrite it as:
minimum coefficient of friction = acceleration / gravity
To calculate the minimum coefficient of friction, we need the value of gravity, which is approximately 9.8 m/s^2.
minimum coefficient of friction = 6.76 m/s^2 / 9.8 m/s^2 ≈ 0.69
Therefore, the minimum coefficient of friction that will prevent sliding on the flat curve is approximately 0.69.