Stopping distance of a car

In summary: Yes. Do you understand why?In summary, the driver of an 1800kg car traveling at 29.0m/s slams on the brakes, locking the wheels on the dry pavement. The coefficient of kinetic friction between rubber and dry concrete is typically 0.600. The stopping distance is found by dividing 756900J by 10584N, which is 42.9 meters.
  • #1
bigtymer8700
40
0
The driver of an 1800kg car traveling at 29.0m/s slams on the brakes, locking the wheels on the dry pavement. The coefficient of kinetic friction between rubber and dry concrete is typically 0.600. Find the stopping distance

ive been trying to this problem forever and i know that Its just I am missing something small but i can't figure out what.

Ive solved for the KE_initial= 756900J and i know K_final= 0 I know i have to use the constant accel. equation
vf^2=vi^2 + 2as. I just don't know how to go about starting the problem all the unknowns have got me confused.

My attempt went like this. I got the F_normal by 1800kg(9.8) to get 17640N.
17640(.600) gave me 10584N which i used as the frictional force.
a=F/m so then 17640N-10584N/1800 =3.92 i used that for acceleration but i got the wrong answer i don't know where I am messing up
 
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  • #2
Energy isn't important in this case. Only speed, mass, force, distance and acceleration. You should have a formula relating them.

You have initial and final speed and mass already. You can find the frictional force. It's the coefficient of friction times the normal force. You know what the normal force is, right? It's the weight of the car.

Now, the frictional force is what's stopping the car, right? So if you know it and know the mass of the car, you can find the deceleration, and you should have a formula to get distance from all of that.
 
  • #3
dont you need the acceleration to get the normal Force?
 
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  • #4
Nope. The mass of the car is 1800kg. To find the force you have to multiply by acceleration. Think of which way the normal force is pointing.
 
  • #5
Normal force is pointing up i got that from my free-body diagram so i did 1800kg(9.8) to get 17640N
 
  • #6
You're off by a zero, but yeah, that's it.

So you have the normal force. So F = u*m*a. That's your stopping force.
 
  • #7
yea I got that far 17640(.600)= 10584N for the stopping force. but how do i go about solving for the acceleration to get the stopping distance?
 
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  • #8
Ok I got some insight on the problem and hopefully this is the way. but i know that W= K_f - K_i. I already know the car is stopping so K_final is 0.
K_i is (.5)1800kg(29m/s)^2 which gives you 756900J. Since you know Work is also W=F * s you got the Work from the KE and F=17640N. you divide 756900J/17640N to get 42.9 is that correct?
 
  • #9
Yes, that works, but I don't understand why you insisted on using energy here. It works here because it's a simple system. If you get something more complicated, energy probably won't be "conserved", so I'd be careful and stick to forces instead.
 
  • #10
Since you know Work is also W=F * s you got the Work from the KE and F=17640N. you divide 756900J/17640N to get 42.9 is that correct?

Shouldn't you be dividing by 10584 N here? That is what the frictional force was found to be. 17640 N is the normal force.
 
  • #11
hage567 said:
Shouldn't you be dividing by 10584 N here? That is what the frictional force was found to be. 17640 N is the normal force.


so to get that distance you have to divide 756900/10584?
 
  • #12
Yes. Do you understand why? The frictional force is what is causing the car to stop, not the normal force.
 

1. What factors affect the stopping distance of a car?

The stopping distance of a car is affected by several factors, including the speed of the car, the condition of the road surface, the condition of the tires, and the reaction time of the driver. Other factors such as weather conditions and the weight of the car can also have an impact on stopping distance.

2. How does speed affect the stopping distance of a car?

The higher the speed of a car, the longer the stopping distance will be. This is because the car has more kinetic energy, which means it will take longer for the brakes to slow it down. As a general rule, for every 10 mph increase in speed, the stopping distance will double.

3. Does the type of tires on a car impact stopping distance?

Yes, the type and condition of tires can have a significant impact on the stopping distance of a car. Worn or underinflated tires will have less grip on the road, making it harder for the car to stop. Additionally, different types of tires (such as summer tires vs. winter tires) are designed for different road conditions, which can also affect stopping distance.

4. How does reaction time affect the stopping distance of a car?

The reaction time of a driver is the time it takes for them to perceive a hazard and react by applying the brakes. The longer the reaction time, the longer the stopping distance will be. This is why it is important for drivers to stay alert and focused while behind the wheel.

5. Can the stopping distance of a car be calculated?

Yes, the stopping distance of a car can be calculated using a formula that takes into account the speed of the car, the reaction time of the driver, and the braking distance. However, it is important to note that this calculation is an estimate and may not always accurately reflect the actual stopping distance of a car in real-life situations.

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