Calculating Minimum Car Stopping Distance on a Rainy Day

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Homework Help Overview

The discussion revolves around calculating the minimum stopping distance of a car on a rainy day, given its speed and the coefficient of friction. The problem is situated within the context of kinematics and dynamics, particularly focusing on the effects of friction on motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine whether to use equations of motion or Newton's second law. There is uncertainty regarding the necessity of the car's weight, which is not provided.
  • Some participants suggest using constant acceleration equations, while others clarify the relationship between friction and acceleration, noting that the car's mass is irrelevant to the stopping distance calculation.
  • There is a correction regarding the interpretation of the car's speed, questioning whether it was meant to be acceleration instead.

Discussion Status

The discussion is active, with participants providing insights into the relationships between forces and motion. Some guidance has been offered regarding the use of equations of motion and the irrelevance of mass in this context. However, there is still some confusion about the specific requirements of the problem, particularly regarding the distinction between distance and time.

Contextual Notes

Participants note the lack of information about the car's weight and the potential misunderstanding of the given speed as acceleration. The problem's context is complicated by the rainy conditions affecting friction.

conno719
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A car is traveling down a flat highway at 11.39 m/s(squared), if the coefficient of friction is .100 (its a rainy day) what is the minimum distance in which the car will stop?

Im not sure whether to start with an equation of motion or use F(x)= ma(x).
Just a little confused. I am not sure if the weight of the car is needed, but it is not given...
 
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Since the car is sliding the acceleration is assumed to be constant. This means you can use the constant acceleration equations of motion.

v = v0 + at

Relating the stopping force (opposing friction) to Newton's second law gives us

-fk = ma

Solving for a gives

a = -fk/m

Remembering that fk = uk*Fn we can substitute that into the previous equation and get

a = -uk*Fn / m

The normal force Fn = the cars mass time g, which gives

a = -uk*mg / m which reduces to a = -uk*g

As you can see the mass of the car is irrelevant.

Now solve the constant acceleration equation that was first given for t using a that was just found. Remeber that the final velocity will be zero since the problem wants to know how long it will take to stop the car.
 
thank you for the help
 
Sorry, I just noticed that the question was asking for the distance and not time. So you'll have to use the time you just found to find the displacement using one of the other constant acceleration equations of motion.

x = v0*t + (1/2)*a*t^2 should do it.

BTW I assumed that 11.39 was the velocity in m/s and not the acceleration in m/s^2 (you have 11.39 m/s(squared) written).

If this is not the case then the answer will be different.
 

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