Homework Help: Problem in mechanics

1. Jun 19, 2010

the_storm

1. The problem statement, all variables and given/known data
A race car starts from rest on a circular track. the car increases its speed at a constant rate at as it goes once around the track.

2. Relevant equations

Find the angle that the total acceleration of the car makes- with the radius connecting the centre of the track and the car- at the moment the car completes the circle.

3. The attempt at a solution
First I put the angle = $$\theta$$
I put the total acceleration = a
and then I found that Cos$$\theta$$=$$\frac{a r }{a}$$
then I said ar=$$\frac{v2}{r}$$
and v2=$$\frac{2 by r}{T}$$ where T is the period. But I stopped I have no numbers
So can any one help me?

2. Jun 19, 2010

Staff: Mentor

Do this: Call the tangential acceleration at. Use this to figure out the speed at the end of circle and thus ar. Use those components to find the angle. (Hint: Express everything in terms of the final speed and the radius.)

3. Jun 19, 2010

the_storm

Got it :)
thank you bro :D

4. Jun 19, 2010

the_storm

hey Doc Al am just typing the answer to make sure it is okay, cause I think there is something error because the final answer unreasonable
This what I have done
since at=$$\frac{Vf2}{2\pi r}$$
and ar=$$\frac{vf2}{r}$$
therefore tan$$\theta$$= $$\frac{at}{ar}$$
therefore tan$$\theta$$= $$\frac{v2}{4\pi r}$$ × $$\frac{r}{v2}$$
So $$\theta$$ = tan-1($$\frac{1}{4 \pi}$$
So $$\theta$$ = 4.548 degrees
I think the angle is too small and it is incorrect !! ?

5. Jun 19, 2010

Staff: Mentor

That answer sounds right to me.

FYI: Your formatting is getting messed up because you are using the sup and sub tags within Latex; keep them separate. The way to use subscripts in Latex is like a_r; to use superscripts, v^2.

6. Jun 19, 2010

the_storm

Ok thank you bro very much :)