Finding minimum distance to stop using friction and velocity

In summary, the problem asks for the minimum distance a car traveling at 44.4 mi/h on a rainy day will stop, given a coefficient of friction of 0.13 and an acceleration of gravity of 9.8 m/s2. Using kinematic equations, the solution is D= v0^2/2μg.
  • #1
trivk96
47
0

Homework Statement



A car is traveling at 44.4 mi/h on a horizontal
highway.
The acceleration of gravity is 9.8 m/s2
.
If the coefficient of friction between road
and tires on a rainy day is 0.13, what is the
minimum distance in which the car will stop?
(1 mi = 1.609)
Answer in units of meters

Homework Equations


x=xo+vot + at2
Ff=μ*Fn

The Attempt at a Solution



I honestly have no idea
 
Last edited:
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  • #2
I'd use the kinetic energy work theorem. You learn that yet?
 
  • #3
or you could use basic kinematic equations to solve this.
 
  • #4
Haven't learned kinetic energy work theorems. Could you help me through the easier process. I have a test tomorrow and I want to understand this.
 
  • #5
adding kinetic energy theorem to the problem basically takes into account mass while kinematic equations still hold true. I'd rather go into the kinematic equation realm. Basically, this is asking you what the acceleration of the car is and what distance the car travels if an initial velocity is 44.4mi/h. Convert that to meters/second.
 
  • #6
and if you are ready for the test, then you'll use V^2=V0^2 + 2ax to get the x I mean the right answer.
 
  • #7
[itex]D=\frac{v_{o}^{2}}{2μg}[/itex]

I believe that is the equation.
 
  • #8
i raid is correct!
 

1. What is the minimum distance needed to stop using friction and velocity?

The minimum distance needed to stop using friction and velocity will depend on several factors, including the initial velocity, the coefficient of friction, and the mass of the object. It can be calculated using the equation: d = v^2 / (2 * u * g), where d is the minimum distance, v is the initial velocity, u is the coefficient of friction, and g is the acceleration due to gravity.

2. How does friction affect the minimum stopping distance?

Friction plays a crucial role in determining the minimum stopping distance. The higher the coefficient of friction, the more force will be needed to stop the object, resulting in a longer stopping distance. On the other hand, a lower coefficient of friction will require less force and therefore result in a shorter stopping distance.

3. Can the minimum stopping distance be reduced by increasing the initial velocity?

Yes, increasing the initial velocity will result in a shorter minimum stopping distance. This is because the kinetic energy of the object will be higher, and more force will be required to stop it. However, it is essential to consider other factors, such as the coefficient of friction, as increasing the initial velocity may also increase the stopping distance if the coefficient of friction is high.

4. How does the mass of the object affect the minimum stopping distance?

The mass of the object also plays a significant role in determining the minimum stopping distance. A heavier object will have more inertia, and therefore more force will be required to stop it, resulting in a longer stopping distance. On the other hand, a lighter object will require less force and therefore result in a shorter stopping distance.

5. Is the minimum stopping distance affected by the surface on which the object is moving?

Yes, the surface on which the object is moving can have a significant impact on the minimum stopping distance. A rough surface will result in a higher coefficient of friction, requiring more force to stop the object and resulting in a longer stopping distance. A smooth surface, on the other hand, will result in a lower coefficient of friction and a shorter stopping distance.

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