Determine the tangential and radial acceleration of the car

[kblue!1]

Homework Statement

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 250 km/h in a semicircular arc with a radius of 230 m.

Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.

r=230m
v₁=0 m/s
v₂= 250km/h --> 69.44m/s

Homework Equations

a=r $$\alpha$$

V_tangent=$$\sqrt{\frac{GM}{r}}$$

The Attempt at a Solution

w₁= $$\frac{v1}{r}$$=0

w₂=$$\frac{v2}{r}$$=$$\frac{69.44m/s}{230m}$$=0.302rad/s

(.302)²= 0² + 2 ($$\pi$$/2) $$\alpha$$

$$\alpha$$ = .02903 radan/s²

I got this for my TANGENT: (230m)(.02903radan/s²) = 6.68m/s²

and this is my RADIAL:$$\alpha$$ = 0.0290m/s²

I'm not sure if I did the problem right. My answers seem wrong. Please help me =]

 

[alphysicist]

Hi kblue!1,

Homework Statement

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 250 km/h in a semicircular arc with a radius of 230 m.

Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.

r=230m
v₁=0 m/s
v₂= 250km/h --> 69.44m/s

Homework Equations

a=r $$\alpha$$

V_tangent=$$\sqrt{\frac{GM}{r}}$$

The Attempt at a Solution

w₁= $$\frac{v1}{r}$$=0

w₂=$$\frac{v2}{r}$$=$$\frac{69.44m/s}{230m}$$=0.302rad/s

(.302)²= 0² + 2 ($$\pi$$/2) $$\alpha$$

The speed of .302rad/s corresponds to when the car has moved through the semicircular path, so I don't think the angle is pi/2 here.

$$\alpha$$ = .02903 radan/s²

I got this for my TANGENT: (230m)(.02903radan/s²) = 6.68m/s²

and this is my RADIAL:$$\alpha$$ = 0.0290m/s²

The alpha value is the angular acceleration; the radial acceleration that the question asks for is related to the radius and the angular velocity. What formula does it have?

 

[kblue!1]

Thanks for replying alphysicist :)

the formula for radial acceleration is V^2/r

The speed of .302rad/s corresponds to when the car has moved through the semicircular path, so I don't think the angle is pi/2 here.

Is it just pi?

 

[alphysicist]

Thanks for replying alphysicist :)

the formula for radial acceleration is V^2/r



Is it just pi?

Yes, it would be pi (since the speed of 0.302 rad/s is after the car has moved through an angle of pi).


The radial acceleration is v^2/r like you have; this is also equivalent to

$$a_r=r\ \omega^2$$
so you can find either v or $\omega$ at the halfway mark, whichever you prefer.

 

[kblue!1]

Thank you for your help!