# Homework Help: Vertical acceleration due to car going over speed bump

1. May 14, 2013

### Complete

1. The problem statement, all variables and given/known data
Find the vertical acceleration of a car going over a speed bump a foot wide and 4 inches tall.

2. Relevant equations
Acceleration = dv/dt

3. The attempt at a solution
http://imgur.com/55t2WCQ

I am getting an answer that is around 25*g
I know this is way too much.
neglecting the shocks on the car, what assumptions am I messing up that would allow me to do this problem correctly? This isn't homework, rather a small part of a larger project where I need the forces to do failure analysis.

Last edited: May 14, 2013
2. May 14, 2013

### SammyS

Staff Emeritus

Was that 20 mph speed given ?

Was anything else given, which you have not included here?

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3. May 14, 2013

### Complete

Nothing was given other than the thing I am designing should be able to withstand the force of going over a speed bump. I originally had it at 30mph but my number was way higher so I lowered it hoping that would be my problem. I looked up online the higher end dimensions of a speed bump and got a smaller width of 1 foot and a height of no more than 4 inches. Thanks for the reply.

4. May 14, 2013

### CWatters

Last edited: May 14, 2013
5. May 14, 2013

### Complete

Yes, but speed bumps and speed humps are different. Also I was assuming I should use the bump where the force would be greatest. maybe I was going too high with 4'' but http://www.innoplast.com/sbs6.html was closer to what I was imagining going over.

6. May 14, 2013

### Complete

r = (4² + ¼*12²)/2*4 =6.5
Yes, but I see naught where you are going with this?

7. May 14, 2013

### CWatters

8. May 14, 2013

### CWatters

I was going to work out the acceleration another way but the small radius caught my eye. If curved as per the original drawing it would have very steep sides - perhaps not as bad as a vertical kerb but still.

9. May 14, 2013

### CWatters

Article here suggests humps are typically designed to reduce speeds to 15mph where as bumps target around 5mph.

http://www.dmgov.org/Departments/Engineering/PDF/FAQ9_Speed_Bumps_and_Humps.pdf

10. May 14, 2013

### Complete

11. May 14, 2013

### Complete

Fixed it and I got 5.4g as my maximum acceleration vertical. Thanks again.

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12. May 14, 2013

### haruspex

Sure, but acceleration of what? The tyres, certainly, but a bit less for the wheel as a whole and much less for the vehicle as a whole.
Also, passenger discomfort is not just a matter of peak acceleration. It's a compound oscillator problem. With a short bump, a low speed can produce a much larger amplitude rise in the vehicle than a higher speed.