Car negotiating a banked curve - centripetal force

[frasifrasi]

Car negotiating a banked curve -- centripetal force

We were asked to calculate the optimum (no friction), maximum, and minimum speeds alowed for a car making a banked curve.

I calculated the optimum and maximum velocities using the provided angle, radius, and coefficient of static firction. But how am i supposed to calculate the minimum speed? Should I set the frictional force in the free body diagram pointing towards the bank(outside of curve)? Any suggestions?

Also, we are asked to draw the trajectory of the car going at maximum speed given a coefficient of kinetic friction. Since the friction equations are the same, should I just plug in this coefficient of kinetic friction in place of the old coefficient of static friction?

lastly, would it be right to set the path going toward the wall, and crasing like I imagine it to be?

 

[physicolic]

You say:But how am i supposed to calculate the minimum speed?
You can draw a free body diagram. And then see under what conditions the car slips down the banked curve. After that you can think about minimum velocity that will cause a centrifugal force.

 

[physicolic]

Let's stop the car. If the car is at rest, it means that the minimum velocity is zero. Related with the angle of inclination the car can slip down or does not move. So under the condition of slipping there must be a minimum velocity so that the car does not slip.

 

[frasifrasi]

I think they mean the minumum velocity for the car not to slip, hence why it cannot be 0. Would it make sense to just switch the direction of friction on the free body diagram?

Also, we are asked to draw the trajectory of the car going at maximum speed given a coefficient of kinetic friction. Since the friction equations are the same, should I just plug in this coefficient of kinetic friction in place of the old coefficient of static friction?

 

[Doc Al]

I calculated the optimum and maximum velocities using the provided angle, radius, and coefficient of static firction. But how am i supposed to calculate the minimum speed? Should I set the frictional force in the free body diagram pointing towards the bank(outside of curve)?

The friction force in the case of minimum speed is in one direction (which?) while in the case of maximum speed it is in the opposite direction. Play around with a free body diagram until that clicks.

 

[frasifrasi]

I said that the direction of friction the maximum velocity was toward the center. If the minimum is the opposite, should it be toward the bank (like i thought)?

Can you confirm this?

Also, can anyone help me with the last questions?

 

[Doc Al]

I said that the direction of friction the maximum velocity was toward the center. If the minimum is the opposite, should it be toward the bank (like i thought)?

Can you confirm this?

You are correct. This should make sense. Imagine no friction. If you go too fast, you'll slide up the ramp; too slow, down the ramp. Friction acts to prevent such sliding.

Also, can anyone help me with the last questions?

Not sure what they are looking for.