Unbanked and Banked Curves

[kingwinner]

I have trouble understanding some unbanked and banked curve concepts, can somebody please explain? Thank you for all your help! :Exclamati

 

1)

This is the free body diagram of a car at maximum speed that can safely make a right turn along an unbanked curve (or arc). I don't understand why the frictional force is directed in the direction shown on the diagram. Frictional force opposes the tendency of motion and the tendency of motion of the car should be tangential to the circle...the tendency of motion of the car is not outward away from the cricle, right?

 

 

2)

This is the free body diagram of a car at a speed that can safely make a right turn along a BANKED curve (or arc). (without friction)

Can someone explain why in this case, all the VERTICAL components of forces sum up to zero? (i.e. N cos(theta) = mg) I recall those incline problems like a skier sliding downhill, the components of forces in the direction perpendicular to the INCLINE sum up to 0, but NOT in the vertical direction...this brings me to a deep confusion.........

 

 

3) For the case in question 2, the radius is actaully measured horizontally from the car to the center of the arc. Why shouldn't the radius be measured PARALLEL to the incline?

And why is the centripetal force also horizontal instead of parallel to the incline?

(I can probably survive these questions on a test, but I don't understand the logic and concepts behind it........)

 

 

4) A 2 kg rock is tied to a rope 1m long and swung in a horizontal circle. The rope makes an angle of 30 degrees with the horizontal while it's spinning at a particular rate. Find the tension in the rope and the period of the rock's revolution.

[The trouble to me is the 30 degrees thing...Should I consider the radius as horizontal distance, or should I just use 1m? Assuming the first case, I got tension=39.2N and Period=1.42s, are they correct?]

[Jay-qu]

1)

This is the free body diagram of a car at maximum speed...

 

Well if you did have the frictional force where you suggest what would happen? There would be no circular motion.. the friction points radially inwards to the point that is the center of curvature for that turn. This creates the net force needed to produce the acceleration needed for circular motion to occur ;)

[Lsos]

I see what he's saying with the direction of the fricional force. By definitions that I have seen, frictional force is supposed to oppose the tendency of motion....and yet in this example, it doesn't. It opposes the tendency of motion at a right angle. I understand that this is necessary for the car to turn and whatnot, but it seems to go against the definition. Could the definition be wrong?