Find friction from stopping distance and initial speed.

[Sneakatone]

According to test performed by the manufactures, an automobile with an initial speed of 75 km/h has a stopping distance of 25 m on a level road. assuming that no skidding occurs during breaking, what is the value of μ , between the wheels and the road required to achieve the stopping distance?


I don't know how to apporach this

 

[voko]

Assume that the force of friction is constant and depends only on the weight. What is the equation for this force?

Then, what is the acceleration due to this force?

 

[Sneakatone]

Mg=F?

 

[voko]

Have you heard about the coefficient of friction? What is μ in the problem?

 

[Sneakatone]

Do you mean F=-kx?

 

[voko]

That is not the force of friction.

 

[lep11]

Just use the work-energy theorem.

 

[Sneakatone]

you mean KE=1/2mv^2?
but I am not given a mass only velocity n stopping distance

 

[voko]

Just assume the mass is some m. It will, as usual, drop out eventually.

What you really need to do is recall what the force of friction is.

 

[Sneakatone]

force of friction is unknown

 

[rcgldr]

As Voko implied, assume that the acceleration is constant (and negative since it slows down the car). What is the equation for constant acceleration?

 

[voko]

force of friction is unknown

It is unknown. But you have to assume it is known and it related to the weight. Recall how the force of friction depends on the weight.

 

[Sneakatone]

F=ma

 

[rcgldr]

F=ma

For this problem, F, m, and a are constant. What is the equation for distance with constant acceleration and some initial velocity?

 

[voko]

You are guessing, and this is not good. It looks like you need to review the force of friction.

 

[Sneakatone]

please give me a review

 

[rcgldr]

This equation should have been given to you in your class or textbook. It relates distance to initial velocity and constant acceleration, using x to represent the final position, and x₀ to represent the initial position. (The total distance traveled = x - x₀). You can assume that x₀ is zero for this problem.

x = x₀ + v₀ t + 1/2 a t²

 

[voko]

What you have here is the force of rolling friction (no skidding occurs). It is also known as rolling resistance. The force is ## F_r = \mu N ##, where ## \mu ## is the coefficient of friction that you are supposed to find, and ## N ## is the normal force.

 

[Sneakatone]

I thought about that equation but what should be the inputs for acceleration and time.
im guessing to get time you can do d/v=t

 

[rcgldr]

I thought about that equation but what should be the inputs for acceleration and time.

Those aren't inputs. You're given distance and the initial velocity, and the fact that the final velocity is zero. You'll need to solve for acceleration and time. You need a second equation for velocity versus time, where you know that the final velocity v is zero and v₀ is the initial velocity (75 km/h):

v = v₀ + a t

for distance (which you are told is 25 m):

d = v₀ t + 1/2 a t²

These equations should have been given to you in your class or textbook.

 

[Sneakatone]

so,
20 m/s=-at
20/9.81=2.03s
25=75(2.03)+0.5a(20.3)^2, a=-0.61

 

[rcgldr]

so,
20 m/s=-at
20/9.81=2.03s

9.81 is 1 g of acceleration. At this point, you don't know what the acceleration is, so you need to use both equations, in order to solve for two variables. You'll need to use one of the equations to express acceleration as a function of time or vice versa, then substitute that function for the variable in the second equation, which will then let you solve for the other variable. Then it will be back to the first equation to solve for the first variable.

 

[Sneakatone]

So for the equation v=v0+at i should solve for t instead of a?

 

[rcgldr]

So for the equation v=v0+at i should solve for t instead of a?

You can solve for either a or t (solve for a in terms of t or solve for t in terms of a), then use the result to substitute for a or t in the second equation. Try both ways, one may end up being easier than the other. You should use the given values for this first equation v = v0 + at => 0 = 75 km/h + at. You'll need to convert km/h to m/s (meters per second).