00:01
Hi there, so for this problem, we are told that a car is rounded at 230 meters on a banked circular track.
00:09
So the radius in this case is 230 meters.
00:14
And if the coefficient of static friction between the tires and the road is given, and that is equal to 0 .96.
00:25
The question in here is, what is the maximum speed in meters per second at which the drive can round the track without sliding.
00:34
So we need to find that speed.
00:38
So in this case, we are going to have that.
00:43
First, we can assume the forces that are happening on this car.
00:49
Let's just draw the car in this situation.
01:03
And then we're going to have a force, which is the force that maintains this into the circular.
01:17
Into the centripetal force, and this we have a normal force and the mass of this.
01:26
Now, the sum of forces in the y direction give us that the normal force should be equal to the mass times the acceleration due to gravity because the car is not moving in that direction.
01:38
And then for the sum of forces in the x direction, we are going to have that.
01:45
The centripetal force should be equal to the frictional force, and that's because they need to cancel in order to maintain the car in that position without sliding.
02:01
So with that said, we know that the centripetal force is defined as the mass times the speed squared divided by the radius, and the friction force is defined as the coefficient...