Uniform Circular Motion on a race track

In summary, the conversation discusses finding the smallest and largest speeds at which cars can move on a banked race track without relying on friction. The radius of the smallest circular path is 116 m and the radius of the largest path is 153 m, with a height of the outer wall at 11.6 m. The conversation suggests thinking about the physics and drawing a free-body diagram to determine the forces and where the resultant force should point. Equations should then suggest themselves to solve for the speeds.
  • #1
Physicsnoob90
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Homework Statement


On a banked race track, the smallest circular path on which cars can move has a radius of 116 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.6 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.

Homework Equations

The Attempt at a Solution


I'm stuck on what type of equation to use since i don't know what to do with the given height? What am i supposed to treat it as? Can anyone help me out?
 
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  • #2
Before looking for equations - try thinking about the physics.

What effect does the height have on the track?
Where, on the track, will the cars be able to travel at the fastest speed (all else remaining equal)?

Start out by drawing a free-body diagram ... what are the forces? Where do they point? Where should the resultant force point?

Once you've done that - some equations should suggest themselves.
 

1. What is uniform circular motion?

Uniform circular motion is the motion of an object along a circular path at a constant speed. This means that the object maintains the same speed throughout the motion, but its direction changes as it moves along the circular path.

2. How is uniform circular motion different from regular circular motion?

In regular circular motion, the speed of the object may vary as it moves along the circular path. In uniform circular motion, the speed remains constant, while the direction changes.

3. How is uniform circular motion related to a race track?

A race track is a perfect example of uniform circular motion, as the cars move along the track at a constant speed while changing direction along the curved path.

4. What is the role of centripetal force in uniform circular motion on a race track?

Centripetal force is necessary to keep an object moving in a circular path. In the case of a race track, the centripetal force is provided by the friction between the tires of the car and the track, allowing the car to maintain its speed and direction along the curved path.

5. Is the speed of a car the only factor in uniform circular motion on a race track?

No, the radius of the circular path and the mass of the car also play a role in determining the centripetal force and the overall motion of the car on the track. A larger radius or a heavier car will require a greater centripetal force to maintain uniform circular motion.

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