Solve Problem in Mechanics Homework: Find Acceleration Angle

[the_storm]

Homework Statement

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.

Homework 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.

The Attempt at a Solution

First I put the angle = $$\theta$$
I put the total acceleration = a
and ar= a radial
and then I found that Cos$$\theta$$=$$\frac{a <span style="font-size: 9px">r }{a}</span>$$
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 anyone help me?

 

[Doc Al]

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

 

[the_storm]

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

Got it :)
thank you bro :D

 

[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 a_t=$$\frac{V_f²}{2\pi r}$$
and a_r=$$\frac{v_f²}{r}$$
therefore tan$$\theta$$= $$\frac{a_t}{a_r}$$
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 ! ?

 

[Doc Al]

So $$\theta$$ = tan^-1($$\frac{1}{4 \pi}$$
So $$\theta$$ = 4.548 degrees
I think the angle is too small and it is incorrect ! ?

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.

 

[the_storm]

Ok thank you bro very much :)