Angular motions and Dynamics - centripetal acceleration

[hussey1]

Hi all ,

I'm new here, studying computer aided product design and in my second year. We do a lot of physics and maths. I am stuck on a current question, probably not too hard but I am struggling to know what to do and the lecturers notes are not very helpful.

Homework Statement

Calculate the maximum speed in km/h at which a train may travel around a bend of 100m radius if the maximum centripetal acceleration must not exceed 0.1g in order to maintain passenger comfort.

Homework Equations

Centripetal acceleration = V^2 / r

2 x Pi x r

radian to degree = X x 180/pi

The Attempt at a Solution

Attempted using above equations and tried different methods the closest I got to the answer is:
2 x pi x r

= 2 x pi x 100

= 628 = 0.628km

0.628 x 180/pie

=35.98

I have the answer but just can't quite get it, the answer is: 35.66 km/h

Other methods I tried are here (I know they are not correct, but I tried anyway):

0.1g= V^2 / r

0.1g = V^2 / 100m

V^2 = 0.1g x 100m

V^2 = 10 (g/m?)

v = Square root of 10

V = 3.16

I also used the same as above but put this in the equation 0.1 x 9.81 = 0.981 and I got 0.99

Many thanks in advance
Ollie

 

[Doc Al]

Attempted using above equations and tried different methods the closest I got to the answer is:
2 x pi x r

= 2 x pi x 100

= 628 = 0.628km

0.628 x 180/pie

=35.98

I don't understand what you did here.

This is the equation you need:

Centripetal acceleration = V^2 / r

Set it up and solve for V.

 

[Doc Al]

Other methods I tried are here (I know they are not correct, but I tried anyway):

0.1g= V^2 / r

0.1g = V^2 / 100m

Now you're on the right track. Hint: What is 'g'?

When dealing with these equations, express everything in terms of standard units: meters and seconds. You can convert to other units later.

 

[hussey1]

Thank you, I tried using that equation, and just edited my post above while you were posting, but I still didn't get the right answer?

 

[Doc Al]

Thank you, I tried using that equation, and just edited my post above while you were posting, but I still didn't get the right answer?

Yep. See my comment above.

 

[hussey1]

I tried g as gravity above? I guess this is incorrect is g grams?

 

[Doc Al]

I tried g as gravity above? I guess this is incorrect is g grams?

'g' is the acceleration due to gravity. What does it equal? (Look it up!)

(No, g is not grams!)

 

[hussey1]

Thank you, yes I tried with gravity as above "I also used the same as above but put this in the equation 0.1 x 9.81 = 0.981 and I got 0.99" But I still did not get the correct answer.

I have done this:
0.1g= V^2 / r

0.1x(9.81) = V^2 / 100m

V^2 = 0.981g x 100m

V^2 = 98.1

v = Square root of 98.1

V = 9.9

Also put in as km/h 35.3 and got v= 18.78

 

[Doc Al]

Thank you, yes I tried with gravity as above "I also used the same as above but put this in the equation 0.1 x 9.81 = 0.981 and I got 0.99" But I still did not get the correct answer.

I have done this:
0.1g= V^2 / r

0.1x(9.81) = V^2 / 100m

V^2 = 0.981g x 100m

V^2 = 98.1

v = Square root of 98.1

V = 9.9

Good! The speed here is in standard units of m/s; you'll need to convert to km/hr.

 

[hussey1]

Thank you, I appreciate the help! Got the answer now!

I think I was thinking it was more complex than it actually was and thinking into it too much!

Thank you again!