Determine the tangential and radial acceleration of the car

AI Thread Summary
The discussion focuses on calculating the tangential and radial acceleration of a car accelerating uniformly in a semicircular arc at the Indianapolis 500. The car accelerates from rest to 250 km/h (69.44 m/s) with a radius of 230 m. The tangential acceleration was calculated to be 6.68 m/s², while the radial acceleration formula was clarified as v²/r, leading to the conclusion that it is equivalent to rω². The participants emphasized the importance of using the correct angle for calculations, confirming that the car's position halfway through the turn corresponds to an angle of π radians. Accurate application of these equations is crucial for determining the correct accelerations.
kblue!1
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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

Vtangent=\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 =]
 
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Hi kblue!1,

kblue!1 said:

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

Vtangent=\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?
 
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?
 
kblue!1 said:
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

<br /> a_r=r\ \omega^2<br />
so you can find either v or \omega at the halfway mark, whichever you prefer.
 
Thank you for your help!
 
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