Banked Circular Motion with Static Friction

In summary, the conversation discusses the calculation of the coefficient of static friction for a car not to skid when traveling at different speeds on a properly banked curve. The solution involves finding the angle of the curve, which is calculated to be 21.4 degrees, and then using the equation FNsin(theta) + musFN to determine the centripetal force needed for circular motion.
  • #1
milky9311
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Q: "If a curve with a radius of 85m is properly banked for a car traveling 65km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95km/h?"

[PLAIN]http://a4.sphotos.ak.fbcdn.net/hphotos-ak-ash4/215513_1974874979462_1470693940_32310002_1293630_n.jpg


2. The attempt at a solution

I found theta

FNcos(theta) = mg

(mgsin(theta))/cos(theta) = (mv2)/r

theta = 21.4o

But next bit i couldn't do.

Wouldnt the centripetal force of the 95km/h car be FNsin(theta) + musFN? as the static friction + the horizontal component of the normal force allows circular motion?

thanks
 

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  • #2
milky9311 said:
FNcos(theta) = mg


FNcos(theta) = mg??:confused: Check that again...
 

1. What is banked circular motion with static friction?

Banked circular motion with static friction refers to the motion of an object moving in a circular path on a banked surface, such as a curved road or a banked track. Static friction is the force that allows the object to maintain its speed and direction as it moves along the banked surface.

2. How is the banked angle related to the speed of the object?

The banked angle, also known as the angle of inclination, is directly related to the speed of the object. As the speed of the object increases, the banked angle must also increase in order for the object to maintain its circular path without slipping or sliding.

3. What is the role of static friction in banked circular motion?

Static friction plays a crucial role in banked circular motion as it provides the necessary centripetal force for the object to stay on its circular path. Without static friction, the object would slide or slip off the banked surface due to the centrifugal force acting on it.

4. How does the mass of the object affect banked circular motion with static friction?

The mass of the object does not have a significant effect on banked circular motion with static friction. As long as the object has enough mass to generate sufficient normal force and static friction, it will be able to maintain its circular path at a given speed and banked angle.

5. What happens if the banked angle is too steep or too shallow?

If the banked angle is too steep, the object will experience a larger centripetal force than necessary, causing it to travel in a smaller circle or even leave the banked surface. If the banked angle is too shallow, the object will not have enough centripetal force and may slide or slip off the banked surface. The ideal banked angle is one that allows the object to maintain a constant speed and circular path without slipping or sliding.

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