Stopping distance considering coefficient of friction

In summary, you are having trouble with the equation relating the force F, the mass m, and the acceleration a of an object. You use the second equation to find the time it takes to stop, and then plug that into the first equation to get the distance. You get the same answer using either method.
  • #1
Aubiefan
16
0
I am having a lot of trouble with this problem:
A car is traveling at 45.0 km/h on a flat highway. If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?
I know it uses the delta X kinematics equation, so I should use friction to figure out the acceleration, but we haven't covered this material in class and I am at a loss for how to proceed. Also, will I be considering four systems, one for each tire in contact with the road?
Thanks, any tips are appreciated!
 
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  • #2
What equation do you use to relate the frictional force F to the coefficient of friction mu and the normal force (weight) N? Even though N points down, which direction does the force F of friction point? And no, you don't need to do all 4 wheels, because you would just get 1/4 the force at each, which adds up to 1 for all of them. Show us your work and we can help guide you if you need help.
 
  • #3
The frictional force (F) is mu times the normal force, but I don't know what the mass or weight of the car is, that iis one main thing that is confusing me. I am given the coefficient, so I have F= (0.1)n, which can be rearranged to 0.1=n/F, or 0.1=applied force/frictional force. So I know that frictional force is ten times the applied force, but I am still not sure what equation to use to try and get acceleration from that. Any tips on the best equation to use here?
Thanks for clearing up the issue about the four wheels, I appreciate it!
 
  • #4
Aubiefan said:
The frictional force (F) is mu times the normal force, but I don't know what the mass or weight of the car is, that iis one main thing that is confusing me.
Hint -- the mass of the car will cancel out of the equation. Set up the equation with the frictional force being the decelerating force. What is the equation of motion relating the force F, the mass m, and the acceleration a of an object?
 
  • #5
I know that F=ma, so if F equals ma, so I would think that ma=0.1n, meaning acceleration is 0.1n/m. I also know that n=mg, so ma=0.1(mg), now I see where mass cancels out, thanks for the hint.
So I set a=(0.1)g, and got a=.98. I plugged that into V^2=Vo^2 + a(delta X), with 12.5 m/s^2 as Vo (my starting speed, converted from km/hr) and V=0. I solved for delta X, and got 76.56. When I typed it into my Webassign answer sheet, it told me it was incorrect but within 10% of the right answer. Any idea where I have gone wrong?
thanks for your patience!
 
  • #6
> V^2=Vo^2 + a(delta X), with 12.5 m/s^2 as Vo

First, a typo -- the units of velocity are m/s. Second, the full equation for motion is

[tex]d = d_0 + v_0 t + \frac{a t^2}{2}[/tex]

[tex]v = v_0 + a t [/tex]

Use the 2nd equation to find the time it takes to stop, then plug that into the first one to get the distance. What answers do you get?


EDIT -- fixed a couple LaTex typos
 
  • #7
I finally got it! I solved it using your method, and then tried the first method again and got the same answer, I guess I had been punching something into the calculator wrong. My final answer was 79.7 m.

Thank you so much for your help and your patience, it is EXTREMELY appreciated!
 

FAQ: Stopping distance considering coefficient of friction

1. What is stopping distance?

Stopping distance is the distance a vehicle travels from the moment the brakes are applied until it comes to a complete stop.

2. What is coefficient of friction?

Coefficient of friction is a measure of the amount of friction between two surfaces in contact with each other. It is a dimensionless number that represents the ratio of the force required to move one surface over the other to the force pressing the two surfaces together.

3. How does coefficient of friction affect stopping distance?

The coefficient of friction plays a crucial role in determining stopping distance. It determines how much force is needed to stop a vehicle and how quickly it will decelerate. A higher coefficient of friction means a stronger grip between the tires and the road, resulting in a shorter stopping distance.

4. What factors affect coefficient of friction?

The coefficient of friction can be affected by various factors such as the type and condition of the road surface, the type and condition of the tires, the weight and speed of the vehicle, and weather conditions.

5. How can we calculate stopping distance considering coefficient of friction?

To calculate stopping distance, we need to know the initial speed of the vehicle, the coefficient of friction between the tires and the road, and the deceleration rate of the vehicle. The formula for calculating stopping distance is: stopping distance = (initial speed)^2 / (2 x coefficient of friction x deceleration rate). However, this is a simplified formula and does not take into account other factors such as reaction time and vehicle conditions. It is always best to follow safe driving practices and maintain a safe distance from other vehicles to prevent accidents.

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