Determine the maximum theoretical speed expected for a car

1. Jun 27, 2009

Apprentice123

Determine the maximum theoretical speed expected for a car, leaving the rest, covering a distance of 50m. The coefficient of static friction between tire and road is 0,80. Knowing that the front wheels bear 60% of the weight of the car and the back, the remaining 40%. Determine the speed (a) traction front (b)
traction back

(a) 78,1 Km/h
(b) 63,8 Km/h

2. Jun 27, 2009

LowlyPion

Re: Dynamic

3. Jun 27, 2009

Apprentice123

Re: Dynamic

The answers are in the book. I do not understand the problem

4. Jun 27, 2009

cepheid

Staff Emeritus
Re: Dynamic

If a car is to reach a final speed vf over a distance of d = 50 m at constant acceleration, then you know from basic kinematics what acceleration, a, is required.

However, the acceleration is the driving force over the mass. In this case, the driving force is equal to the frictional force between the tires and the road (this is what propels the vehicle forward). If the acceleration to reach vf is too high, the tires will not be able to provide enough static friction to support this acceleration, and the tires will slip (we say that the car loses traction).

Therefore, the question is asking what is the maximum allowable vf (at the end of 50 m) that will ensure that the driving tires maintain traction? The answer is different for the front tires and the rear tires, because each set of tires is bearing a different load and is therefore able to provide a different amount of static friction force.

5. Jun 27, 2009

Apprentice123

Re: Dynamic

What is driving force ?
V^2 = Vo^2 + 2a(x - xo)

V = ?
Vo = 0
x - xo = 50
a = How to calculate?

6. Jun 27, 2009

LowlyPion

Re: Dynamic

Consider the friction available through the wheels, to provide motive force for the vehicle. How much of force, given the weight distribution between the wheels and the coefficient of friction through say the back wheels, can the back wheels provide to move the vehicle forward? Keep in mind that if the engine supplies too much power that a great deal of the power will go to burning rubber. So there is an upper limit that you can determine through the weight and friction relationship.

What they want is how fast can it accelerate if power comes from the rear wheels, and then how much if supplied through the front.

7. Jun 27, 2009

Apprentice123

Re: Dynamic

Yes But I do not know which formula I use

8. Jun 28, 2009

cepheid

Staff Emeritus
Re: Dynamic

Two of us have told you that the force propelling the car forward is equal to the FRICTION force between the tires and the road. What is the formula for a friction force?

9. Jun 28, 2009

Apprentice123

Re: Dynamic

Sum of forces (Z)
* u = 0,80

ZFy = 0
N - P = 0
N = P

ZFx = m.a
-N.u + V = m.a
-(m.g.u) + V = m.a
V = a + 7,848

V^2 = (Vo)^2 + 2.a.x
....
a = 84,3 m/s^2

V = 92,148 m/s^2

60% V => 55,288 m/s
40% V => 36,86 m/s

10. Jun 28, 2009

cepheid

Staff Emeritus
Re: Dynamic

No, you cannot have velocity in the force balance equation. Velocity is not a force!

Try this. Newton's Third Law says that if the tires push back on the road, then the road pushes forward on the tires. So the forward force on the car, Fforward is:

Fforward = μN

ΣFx = Fforward = μN = ma

Now you can calculate a.

Be careful! N is not the same for the front wheels as it is for the back wheels.

11. Jun 28, 2009

Apprentice123

Re: Dynamic

Thank you very much

A) (m.g.u.60)/100 = m.a
a = 4,7088 m/s^2

V^2 = (Vo)^2 + 2aX
V = 21,7 m/s => 78,12 Km/h

B) (m.g.u.40)/100 = m.a
a = 3,1392 m/s^2
V = 17,71 m/s => 63,756 Km/h