00:01
So we have a flat unbanked curve on a highway, so a circle like this.
00:09
And this circle has some radius r, where that radius r is equal to 220 meters.
00:20
We're told that a car is going around this curve at a speed of 25 meters per second.
00:28
We want to know in part a, what is the minimum coefficient of friction that will prevent sliding? so to visualize is better, let's imagine we have this car in red right here going around this bank, right? and so if we were to look at a free body diagram of this car, if we were to look at head -on, we would see that the ground is pushing on it with some normal force, the earth is pulling on it with some weight force, and towards the center of the curve is some frictional force, right? because when the car is going around this curve, it wants to move like that, but we don't want it to.
01:18
We don't want it to slide off the curve.
01:21
We want it to stay on the curve.
01:23
When we're talking about circular motion, we know that net force is equal to mass times centripetal acceleration.
01:33
And so if you're wondering why you weren't given a mass, we'll find out in a second.
01:39
The only force acting in the direction of acceleration, because we are accelerating this way, towards the center of the circle, is force of friction.
01:50
So we have force of friction is equal to mass times centripetal acceleration.
01:59
Now we need two things.
02:00
We first know that force of friction is equal to the coefficient of friction times the normal force.
02:14
And because there's no acceleration in the y direction, we know that net force in the y direction will equal zero, which implies that normal force is equal to weight force.
02:26
So that gives us the formula.
02:30
Normal force is equal to weight force, which we know is equal to m g.
02:34
So using these two formulas, we can now plug in here...