What is the Speed of the Train as it Rounds a Curve?

  • Thread starter Thread starter julz3216
  • Start date Start date
  • Tags Tags
    Curve Train
AI Thread Summary
A train traveling at a constant speed rounds a curve with a radius of 218 m, causing a lamp to swing out at an angle of 16.6°. The problem involves calculating the train's speed using the equation for centripetal acceleration. Initial attempts to solve the problem included using incorrect trigonometric functions, but the correct approach involves recognizing the relationship between the vertical and horizontal components of acceleration. The final solution highlights that the centripetal acceleration equals the horizontal component derived from the angle, leading to the correct calculation of speed. Understanding the dynamics of the forces acting on the lamp is crucial for solving this type of problem effectively.
julz3216
Messages
18
Reaction score
0

Homework Statement



A train traveling at a constant speed rounds a curve of radius 218 m. A lamp suspended from the ceiling swings out to an angle of 16.6° throughout the curve. What is the speed of the train?


Homework Equations



mv^2/r


The Attempt at a Solution



I drew a diagram and attempted to calculate v by setting mv^2/r = -cos16.6 mg
I don't really know how to approach this?
 
Physics news on Phys.org
julz3216 said:

Homework Statement



A train traveling at a constant speed rounds a curve of radius 218 m. A lamp suspended from the ceiling swings out to an angle of 16.6° throughout the curve. What is the speed of the train?


Homework Equations



mv^2/r


The Attempt at a Solution



I drew a diagram and attempted to calculate v by setting mv^2/r = -cos16.6 mg
I don't really know how to approach this?

I think the angle is with the vertical, which makes the deflection in x given as Sin16.6 not Cos 16.6.

V2/r = Sin16.6*g

V = (r*sin16.6*g)1/2
 
I tried and got 24.705 but that was wrong. Are there any other ways to approach the problem?
 
julz3216 said:
I tried and got 24.705 but that was wrong. Are there any other ways to approach the problem?

What units do they want the answer in? m/s or km/h?

24.705 m/s = 88.9 km/h
 
I tried both ways but neither options were correct. I think it is supposed to be in m/s and I think my answer is wrong in general, is there anything else I can do to get another answer?
 
Ooops. Sorry. I did a sketch and realized vertical is g and that means then that

V2 = tan16.6*g*r
 
Ok, I got it! Thank you so much.
 
julz3216 said:
Ok, I got it! Thank you so much.

It's important you understand why.

Draw the acceleration vectors. The acceleration vectors add to some resultant a that forms the angle. The vertical component is g which means the Resultant acceleration on the lamp is given by

g = ay = a*cosθ

So a = g/cosθ

For the x component, that means that ax = a*sinθ = g*sinθ/cosθ = g*tanθ

and that is what equals the centripetal acceleration.
 

Similar threads

What Forces Act on a Train Engine Going Around a Circular Curve?
Replies
10
Views
3K
Train collision prevention problem
Replies
8
Views
3K
Car Rounding Curve: Acceleration Calculation with C=2piR
Replies
5
Views
2K
Two decelerating trains on a collision course
Replies
2
Views
2K
1-D Kinematics: Trains and a bird
Replies
20
Views
3K
Calculating Train Speed Using Centripetal Force | 15° Angle, 150m Radius
Replies
3
Views
2K
Man on a railroad car rounding a curve
Replies
5
Views
1K
Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
Replies
30
Views
3K
Calculating Friction Force of Train on Passenger at Curved Track
Replies
14
Views
10K
What velocity does a train need to go up and down the hill
Replies
37
Views
4K

Hot Threads

Recent Insights

Back
Top