And the Ray Hagglund Problem: You are invited as an engineer expert to a court w

Question

And the Ray Hagglund Problem: You are invited as an engineer expert to a court where a speed limit violation incident is considered, The car was travelling at an unknown speed V when a traffic policeman signaled the driver to stop. The driver pressed the brake pedal, thereby locking the wheels and forcing the car into a pure sliding motion until it stopped completely. The duration T of this sliding motion and the corresponding sliding length S are known: T-4 sec and S = 40 meters. The driver argues that the ratio S/T is well within the permitted speed limit 30 miles per hour. Can vou use the available data to estimate the actual value of V for the court ?? and explain the court why it is different from S/T? Also, derive the formula for the coefficient of kinetic friction f (which is assumed to be constant) in terms of S and T. You can certainly integrate (twice) the equation of motion, but it seems simpler to use both well-known first integrals - energy and momentum integrals.

Explanation / Answer

given, time of slide, T = 4 s
length of slide, S = 40 m

S/T = 10 m/s = 22.3684 mph

let the actual speed at the begining of the braking be V
then
0 = V - at ( where s ia deceleration of the car)
V = a*4
a = V/4 .. (1)

also,

2*a*s = V^2
2*V*s/4 = V^2
V = 2s/4 = 2*40/4 = 20 m/s
hence
acual speed of the car before application of breaks = 44.368 mph, which is greater than the sped limit, and hence the person was overspeeding and should be fined

now, a = V/T
V = 2s/T
hence
a = 2s/T^2

also,
for coefficeint of friction
a = u*g
then
u = a/g = 2s/gT^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---