How Is the Shortest Stopping Distance Calculated for a Wet Road?

[94strat]

1. Need help with daughters physics...been 35 yrs since I was in class.

100kg car moves at speed of 29.3m/s on horizontal road
Static CoF = 0.145
Kinetic CoF = 0.1015
Acceleration of gravity = 9.8m/s squared

Road is wet
Neglect Reaction time of driver

What is shortest possible stopping distance for car under these conditions? answer in "m"

2. I think you might star with 2nd law: Fnet=m*a but I can't figure out how to work with the CoF's

 

[lanedance]

in the static case - the maximum sustainable friction froce is, (before the wheels lock up & slide)
F_f = c_s.N

where c_s is the static coefficient of friction, N is the reaction force form teh road on the tires, which in this case will be exactly equal (as it is balancing) to the graviataional force

in the sliding case - the friction force is
F_f = c_k.N

where c_k is the kinetic coefficient of friction

use these to find the acceration to use in the 2nd law

 

[94strat]

Many Thanks!

 

[94strat]

OK...synapse lapse again...

I have Velocity initial (Vi) = 29.3m/s and Velocity final (Vf)= 0ms/

Calculated Ff Static = 1.421 (m/sec sq?)
Calculated Ff Kinetic = 0.9947(m/sec sq?)

Where do I go from here to find the distance?

 

[RoyalCat]

OK...synapse lapse again...

I have Velocity initial (Vi) = 29.3m/s and Velocity final (Vf)= 0ms/

Calculated Ff Static = 1.421 (m/sec sq?)
Calculated Ff Kinetic = 0.9947(m/sec sq?)

Where do I go from here to find the distance?

The units of force are Newton - $$\frac{kg\cdot m}{s^2}$$

You posted the correct formula, you just didn't apply it properly. Look at $$F=ma$$ again.

 

[and9]

OK...synapse lapse again...

I have Velocity initial (Vi) = 29.3m/s and Velocity final (Vf)= 0ms/

Calculated Ff Static = 1.421 (m/sec sq?)
Calculated Ff Kinetic = 0.9947(m/sec sq?)

Where do I go from here to find the distance?

Since the car has an initial velocity (Vi) and is being accelerated by the force of friction which is slowing the car to a final speed of (Vf) of zero, you need to find the acceleration of the car by the formula F=ma where F equals the force of friction static (since the road is wet and the car is sliding), m the mass of the car, and then solve for a. Once you have Vi, Vf, a, you should be able to find the distance traveled through the equation

Vf² = Vi² + 2ad where d is the distance the car travels

 

[94strat]

Thanks to all! I was almost there...just circling around the final. Appreciate the help!

 

[94strat]

Man...have I spent too much time in financial spread sheets today

OK...
Static CoF (Ff-s) = M x a

Ff-s = 0.145 x 9.8m/sec squared = 1.421 m/sec sqrd

1.421 m/sec sqrd = 1000kg x a
1.421 m/sec sqrd / 1000kg = a
0.001421 m kg/sec sqrd = a

Vf sqrd = Vi sqrd + 2ad
(0 m/s) sqrd = (29.3 m/s) sqrd = 2(0.001421 m kg/sec sqrd)(d)
(0 m sqrd/sec sqrd) - (858.49 m sqrd/sec sqrd) = .002842 m kg/sec sqrd(2d)
(-858.49 m sqrd/sec sqrd) / .002842 m kg/sec sqrd = 2d
-302072.48 Label =? = 2d
-151036.24 label =? = d

I'm guessing that utlimatly the stopping distance will be 151.03624m, but I can't seem to rationalize how I would get there...

where am I missing it??

 

[and9]

Man...have I spent too much time in financial spread sheets today

OK...
Static CoF (Ff-s) = M x a

Ff-s = 0.145 x 9.8m/sec squared = 1.421 m/sec sqrd

1.421 m/sec sqrd = 1000kg x a
1.421 m/sec sqrd / 1000kg = a
0.001421 m kg/sec sqrd = a

Vf sqrd = Vi sqrd + 2ad
(0 m/s) sqrd = (29.3 m/s) sqrd = 2(0.001421 m kg/sec sqrd)(d)
(0 m sqrd/sec sqrd) - (858.49 m sqrd/sec sqrd) = .002842 m kg/sec sqrd(2d)
(-858.49 m sqrd/sec sqrd) / .002842 m kg/sec sqrd = 2d
-302072.48 Label =? = 2d
-151036.24 label =? = d

I'm guessing that utlimatly the stopping distance will be 151.03624m, but I can't seem to rationalize how I would get there...

where am I missing it??

You're second part finding the distance is correctly done but with the wrong numbers. Once you correct the numbers plug in the new correct numbers and you'll have correct distance...

For the first part, you are a little off...

First of all we want to find the Ff of the car. We know that Ff=(cof static friction)*N
N=mg = 100*9.8
Ff=.145(N) and for a note of reference, force is measured in Newtons or N (don't be confused with the N represented by normal force)

Once you have Ff, set that equal to F=ma where the force is the Ff we just calculated.
Ff=m*a
Solve for a which is measured in m/s²

Now that you have correct a, refind the distance as you did correctly before.

That should give you the correct answer

 

[94strat]

OK...think I have muddled through

Force = CoF Static )Ff-s x N
Force = 0.145 x (100 x 9.8m/sec sq)
Force = 142.1

F=ma
142.1 = 1000kg x a
0.1421m/sec sq = a

Vf sq = Vi sq =2ad
(0m/sec) sq = (29.3m/sec)sq + 2ad
-858.49 = 2(.1421)2d
-858.49 / .2842 = 2d
3020.73/2 = d

1510.36 m = d

How'd I do??