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A car is traveling at 50.0 km/h on a flat highway. If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum stopping distance in which the car will stop? What is the stopping distance on a dry day when the coefficient is 0.600?

By Ak3183 (Ak3183) on Wednesday, October 29, 2003 - 12:19 am: Edit

you need to find the normal force, so mass of the car is needed.

By Wab (Wab) on Wednesday, October 29, 2003 - 09:08 pm: Edit

Actually, I don't think you need the mass. You want to first find the decceleration from friction. So, hopefully you know that:
force of friction = friction coefficient * normal force
Since there are no vertical forces other than gravity, the normal force would balance out the force of gravity (since there's no net vertical force). So, that means the normal force = acceleration of gravity * mass. So, plug that all back in the equation for the force of friction. Now, you don't have the mass, so you can't complete the equation. But, wait, think for a moment. Hmm... they want a distance, right? And to get the distance you need to use one of those 1-D motion formula things... And they don't have force in any of them. But, wait! There IS acceleration. Now, use Newton's nifty second law... F=ma. You can find the acceleration by just dividing the frictional force by the mass, so you don't need that stinkin' mass! And, what makes it super cool is that friction is the only force in the x-direction, so you don't have weird net force stuff going on.
Now, you want to find the stopping distance. So, think, what do you have and what do you need? You have the initial velocity, it was given in the problem. You just found acceleration. The final velocity should be 0 since the car's stopping. And, you want to find the distance. But, time doesn't really matter in this problem. So, pick the right formula, plug in the digits, and voila!
Any questions?