a dynamics problem

[ahmeeeeeeeeeed]

hello,

 

a problem says

 

http://www.flickr.com/photos/76599498@N07/6895404760/

 

I couldn't know how to start but that's what I did

 

 

http://www.flickr.com/photos/76599498@N07/6895405486/

 

http://www.flickr.com/photos/76599498@N07/6895406078/

 

http://www.flickr.com/photos/76599498@N07/6895403992/

 

 

but I don't think this is the way , since I got the acceleration at a special point .

 

I want to ask some questions

 

1-the acceleration magnitude is variable , due to the variation of the radius od curv. , isn't it ?

 

If so , what is meant by determining the acceleration without specifing a certain moment ?

 

 

2- this problem is under the title ( intrinstic co-ordinates) , If I were to use these co-ordinates what is the key to start with ? I can think of the tangential unit vector to be the same as the direction of the derivative of Y with respect to X , but how to employ this ?

 

 

3- the radius of curv. at some points turned to be negative , is that ordinary or did I just did some calculation wrong ?

[imatfaal]

I couldn't work out what your answers really were. I would look at this problem by thinking that I have an equation that gives me the position in terms of the time (ie almost ignoring the fact that it is a car on a hilly route) - the velocity is the slope of a position time plot - ie first derivative wrt time , the acceleration is the second derivative.

[ahmeeeeeeeeeed]

But it gave me the Y in terms of X , not the position in terms of time

[imatfaal]

but x is in terms of time

[ahmeeeeeeeeeed]

Who said that x is in terms if time ? how ?

[imatfaal]

Who said that x is in terms if time ? how ?

 

I had read the question as giving a horizontal speed of 90kph - which would basically be x in terms of time. But having a closer look it is speed along the bumpy road - I will think again. Apologies

[ahmeeeeeeeeeed]

yes , thanks in advance

[J.Nassar]

Well, since you have a constant speed, we only need to determine the angular acceleration because the linear acceleration is 0. The angular acceleration is the derivative of the angular velocity.

 

 

The angular velocity is the speed divided by the radius of the highway, once you calculated the angular velocity, it should be in X factor, when you get the derivative, it should be a constant number which is the acceleration of the car.