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julz3216
Feb27-09, 01:39 PM
1. The problem statement, all variables and given/known data

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?


2. Relevant equations

mv^2/r


3. 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?
LowlyPion
Feb27-09, 02:42 PM
1. The problem statement, all variables and given/known data

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?


2. Relevant equations

mv^2/r


3. 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
julz3216
Feb27-09, 03:03 PM
I tried and got 24.705 but that was wrong. Are there any other ways to approach the problem?
LowlyPion
Feb27-09, 03:10 PM
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
julz3216
Feb27-09, 03:21 PM
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?
LowlyPion
Feb27-09, 03:33 PM
Ooops. Sorry. I did a sketch and realized vertical is g and that means then that

V2 = tan16.6*g*r
julz3216
Feb27-09, 03:43 PM
Ok, I got it! Thank you so much.
LowlyPion
Feb27-09, 04:30 PM
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.