• Support PF! Buy your school textbooks, materials and every day products Here!

Determine the tangential and radial acceleration of the car

  • Thread starter kblue!1
  • Start date
  • #1
3
0

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 [tex]\alpha[/tex]

Vtangent=[tex]\sqrt{\frac{GM}{r}}[/tex]

The Attempt at a Solution



w1= [tex]\frac{v1}{r}[/tex]=0

w2=[tex]\frac{v2}{r}[/tex]=[tex]\frac{69.44m/s}{230m}[/tex]=0.302rad/s

(.302)2= 02 + 2 ([tex]\pi[/tex]/2) [tex]\alpha[/tex]

[tex]\alpha[/tex] = .02903 radan/s2

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

and this is my RADIAL:[tex]\alpha[/tex] = 0.0290m/s2

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

Answers and Replies

  • #2
alphysicist
Homework Helper
2,238
1
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 [tex]\alpha[/tex]

Vtangent=[tex]\sqrt{\frac{GM}{r}}[/tex]

The Attempt at a Solution



w1= [tex]\frac{v1}{r}[/tex]=0

w2=[tex]\frac{v2}{r}[/tex]=[tex]\frac{69.44m/s}{230m}[/tex]=0.302rad/s

(.302)2= 02 + 2 ([tex]\pi[/tex]/2) [tex]\alpha[/tex]
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.

[tex]\alpha[/tex] = .02903 radan/s2

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

and this is my RADIAL:[tex]\alpha[/tex] = 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?
 
  • #3
3
0
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?
 
  • #4
alphysicist
Homework Helper
2,238
1
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

[tex]
a_r=r\ \omega^2
[/tex]
so you can find either v or [itex]\omega[/itex] at the halfway mark, whichever you prefer.
 
  • #5
3
0
Thank you for your help!
 

Related Threads for: Determine the tangential and radial acceleration of the car

Replies
4
Views
8K
Replies
7
Views
9K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
7
Views
33K
  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
23
Views
5K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
2
Views
2K
Top