Finding the distance given the intital velocity and the coefficient of friction

In summary, the car is traveling at 15.5m/s on a surface with a coefficient of friction of 0.1. The driver sees a boy 125 m ahead and immediately applies the brakes, causing the car to skid to a stop. Using the equations of kinematics and dynamics, the acceleration can be found by dividing the total frictional force by the mass of the car. Once the acceleration is known, the final velocity can be calculated using the equation Vf^2 = Vo^2 + 2ad. This will determine the distance the car travels before coming to a complete stop and whether or not it will hit the boy.
  • #1
lenalee.9520
4
0

Homework Statement


A car is traveling at 15.5m/s travels on a surface where μ=0.1. The driver sees a boy run into the road 125 m ahead. She immedietly applies the brakes, locking the wheel, and skids to a stop. Where will the car be when it stops? (i.e:Will it hit the boy?)

I know I should start by figuring out the acceleration and then use

Vfinal^2=V inital^2 + 2ad

But, I am having trouble finding the acceleration.

Homework Equations


Fnet=ma
Ffriction= μFN
Vfinal^2=V inital^2 + 2ad


The Attempt at a Solution

 
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  • #2
welcome to pf!

hi lenalee.9520! welcome to pf! :smile:

(try using the X2 button just above the Reply box :wink:)
lenalee.9520 said:
… But, I am having trouble finding the acceleration.

call the mass "m"

then find the force, and divide by m :wink:

(the force will be µ times … ? :smile:)
 
  • #3
Well I ended up with

Ffriction= -mgµ

Is this correct?
 
Last edited:
  • #4
call the mass "m" ! :rolleyes:

(it'll cancel out in the end)
 
  • #5
Ffriction= -mgµ

Is what I got...
But how does it cancel out??
 
  • #6
You could identify it as an energy related problem.
 
Last edited:
  • #7
azizlwl said:
You should identify it as an energy related problem.

Well, my teacher told the class that we should only need equations from the kinematics and dynamics unit, so I've been trying to stick to those things. (I have to turn this in, so I would like to follow his instructions as much as possible, for the sake of my mark)
 
  • #8
As tiny-tim said, call the mass 'm'
Then if you apply force to it, what is the acceleration?
 
  • #9
[itex]\sum[/itex]F = ma = [itex]\mu[/itex]kmg
Once you solve for the acceleration, the rest is just a 'timeless' kinematics problem.
Vf2 = 0 = Vo2 + 2aΔx
 
  • #10
lenalee.9520 said:
Ffriction= -mgµ

Is what I got...
But how does it cancel out??

acceleration = Ffriction/m ? :wink:
 

Related to Finding the distance given the intital velocity and the coefficient of friction

1. What is the formula for finding the distance given the initial velocity and coefficient of friction?

The formula for finding the distance is d = V02 / 2μg, where V0 is the initial velocity, μ is the coefficient of friction, and g is the acceleration due to gravity.

2. How do the initial velocity and coefficient of friction affect the distance traveled?

A higher initial velocity will result in a longer distance traveled, while a higher coefficient of friction will result in a shorter distance traveled. This is because a higher initial velocity will result in a greater force, while a higher coefficient of friction will result in a greater resistance.

3. Can the distance be calculated without knowing the initial velocity or coefficient of friction?

No, the distance cannot be calculated without knowing both the initial velocity and coefficient of friction. These variables are necessary in the formula for finding the distance.

4. What units should be used for the initial velocity and coefficient of friction?

The initial velocity should be in meters per second (m/s) and the coefficient of friction is unitless. It is important to make sure that the units are consistent when using the formula.

5. Is the coefficient of friction a constant value?

No, the coefficient of friction can vary depending on the surfaces in contact and other factors such as temperature and pressure. It is important to use the correct coefficient of friction for the specific situation being studied.

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