Uniform cicrcular motion problem

In summary, the problem involves finding the minimum radius of curvature for a train traveling at 216 km/h to limit the acceleration experienced by passengers to 0.045g. The formula a=vsq./r can be used, but the OP is having trouble with their calculations. The correct value for centripetal acceleration should be multiplied by 9.81. The formula can also be written as v^2/r.
  • #1
mikejones2000
18
0
Uniform cicrcular motion problem...please help..

I am currently having an incredibly difficult time on the following homework problem dealing with circular motion. The problem is as follows:

The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h.

(a) If the train goes around a curve at that speed and the acceleration experienced by the passengers is to be limited to 0.045g, what is the smallest radius of curvature for the track that can be tolerated?
(b) At what speed must the train go around a curve with a 1.70 km radius to be at the acceleration limit?

I converted the speed to m/s and tried using a=vsq./r, but keep screwing up, any help would be greatly appreciated!
 
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  • #2
Hi mike, welcome to PF.

I can't see a problem here, perhaps if you show your working we can point out what you are doing wrong. Remember to multiply 0.045 by 9.81 to obtain the centripetal acceleration.

~H
 
  • #3
Centripetal Acceleration can also be written as v^2/r.
 
  • #4
al_201314 said:
Centripetal Acceleration can also be written as v^2/r.

The OP knows this and stated it in his original post;

mikejones2000 said:
[...] and tried using a=vsq./r [..]

~H
 

1. What is uniform circular motion?

Uniform circular motion is the motion of an object in a circular path at a constant speed. This means that the object is moving at a constant speed along the circumference of the circle, and the direction of motion is constantly changing.

2. What are the key equations for solving uniform circular motion problems?

The key equations for solving uniform circular motion problems are centripetal acceleration, tangential velocity, and angular velocity. These can be calculated using the following equations:
- Centripetal acceleration (ac) = v2/r
- Tangential velocity (vt) = ωr
- Angular velocity (ω) = 2πf = v/r

3. How is uniform circular motion different from linear motion?

In uniform circular motion, the object is moving in a circular path at a constant speed, while in linear motion, the object is moving in a straight line at a constant speed. In circular motion, the acceleration is always directed towards the center of the circle, while in linear motion, the acceleration is in the same direction as the velocity.

4. How does the radius of the circle affect the object's motion in uniform circular motion?

The radius of the circle affects the object's motion in two ways. First, a smaller radius means a tighter circle, which results in a larger centripetal acceleration, making the object move faster. Second, a larger radius means a longer distance to travel, which results in a slower angular velocity and tangential velocity.

5. Can an object in uniform circular motion have a constant speed and changing velocity?

Yes, an object in uniform circular motion can have a constant speed and changing velocity. This is because velocity is a vector quantity, meaning it has both magnitude and direction. In circular motion, the direction of the velocity is constantly changing, even though the speed remains the same.

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