00:01
All right, so we have a car going through a turn of radius, we'll call this capital r.
00:06
And the car starts from rest and undergoes a uniform tangential acceleration a until it makes it a quarter of way around the track where it skids off of the track.
00:18
So let's pretend this is my car picture.
00:20
And we want to know from this information, what is the coefficient of static friction between the car and the track? so what we're going to have is the force of friction is going to be like the coefficient of static friction times the normal force of the car, which is just going to be the weight of the car.
00:41
And at the point it slides off, this is going to be equal to the centrival force of the car, which is its mass times its velocity squared over the radius.
00:52
And we can see that the masses cancel out.
00:55
And so mu s is going to be like v squared over r times g but that doesn't get us very far because we don't know what v or r is of course we know what g is but we know v the car is uniformly accelerated um with an acceleration a and we can we know that it travels a distance of basically a quarter of a circle now the total circumference of the track presumably is 2 pi r so the distance it travels we'll call this d, or maybe delta x, is a quarter of this, so pi over two times r...