Uniform Circular Motion Problem

In summary, at a speed of 216 km/h, the track must have a radius of curvature of 933120 km to avoid experiencing an acceleration of 0.050g.
  • #1
MFlood7356
39
0
1. 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 magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (in km) (b) At what speed must the train go around a curve with a 1.08 km radius to be at the acceleration limit? (in km/h)

2. a=v2/r and T=2pir/v

3. I have attempted both part a and part b but I have no success in getting the correct answer. Here are m attempts
a) a=0.05g
r=v2/a
r=2162/0.05= 933120


b) r=1.08km a=0.05g
v=sqrtar
v=sqrt0.05x1.08= 0.232
 
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  • #2
MFlood7356 said:
1. 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 magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (in km) (b) At what speed must the train go around a curve with a 1.08 km radius to be at the acceleration limit? (in km/h)

2. a=v2/r and T=2pir/v

3. I have attempted both part a and part b but I have no success in getting the correct answer. Here are m attempts
a) a=0.05g
r=v2/a
r=2162/0.05= 933120


b) r=1.08km a=0.05g
v=sqrtar
v=sqrt0.05x1.08= 0.232

Your approach is fine, but you need to remember to make sure your units are consistent. Look carefully at them. You can't mix km/h, m, and s like you've done. Also, don't forget that g has a value, you can't just drop it out of your calculation.
 
  • #3
Well I really was confused about g. I couldn't find out a conversion factor for it anywhere. I don't know how to use it.
 
  • #4
I would just leave g as 9.81 m/s2, and convert all the other quantities so they are in meters and seconds. Then do the calculations, then convert the final answer back into km/h.

But if you wanted to convert g to km/h2, you don't need to "find" a conversion factor. Just do it dimensionally using the same relations you would use to convert anything else (1 km = 1000 m, 1 hr = 3600 s, etc).
 
  • #5
Oh okay but I'm still confused on g. Would I multiply 0.05X9.81 to get the correct acceleration?
 
  • #6
MFlood7356 said:
Oh okay but I'm still confused on g. Would I multiply 0.05X9.81 to get the correct acceleration?

1 G = 9.81 m/s^2

so

0.05 G = ?


yes, u only need to multiply
 
  • #7
OKay thank you I got the right answer
 

1. What is uniform circular motion?

Uniform circular motion refers to the motion of an object moving in a circular path at a constant speed. This type of motion is characterized by a constant magnitude of velocity, but a changing direction, as the object moves around the circle.

2. What are the key components of a uniform circular motion problem?

The key components of a uniform circular motion problem are the radius of the circle, the speed of the object, and the time it takes to complete one revolution. These components can be used to calculate the acceleration, centripetal force, and other important quantities.

3. How do you calculate the acceleration in a uniform circular motion problem?

The acceleration in a uniform circular motion problem can be calculated using the formula a = v^2/r, where a is the acceleration, v is the speed, and r is the radius of the circle. This acceleration is always directed towards the center of the circle.

4. What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving in a circular path, and it always points towards the center of the circle. Centrifugal force, on the other hand, is an outward force that appears to act on an object moving in a circular path, but it is actually just an inertial force, and does not actually exist.

5. How does changing the radius or speed affect the motion of an object in uniform circular motion?

If the radius of the circle is increased, the speed of the object must also increase to maintain uniform circular motion. Similarly, if the speed of the object is increased, the radius of the circle must also increase. Changing either the radius or speed will result in a change in the acceleration and centripetal force acting on the object.

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