Frictional Forces and 1D Motion

[Peterson]

INTRODUCTION:
This is a problem from my Introduction to Physical Science class using "Conceptual Physics" 10th Ed.by Paul G. Hewitt

EXACT PROBLEM:
"The coefficient of kinetic friction between a rubber tire and a wet concrete road is 0.5."

PROBLEMS FACED:
a) Find the minimum time in which a car whose initial speed is 30 mi/hr can come to a stop on such a road.
b) What distance will the car cover in this time?

MY THOUGHTS:
I know I have a coefficient of friction & V0 and Vf. Beyond that, I don't know how to look for the time it will take. What equation am I supposed to be using?

 

[denverdoc]

Lets take this a step at a time. To stop, you need a negative acceleration. Assume the brakes are aplied full force as in panic stop.

I still find the fact that speed/velocity never enters the eqn curious: that is the braking force is constant. Whether from 100mph or 5mph the retarding force is the same. So its like a baseball thrown upwards at different speeds.:The stopping distance depends on velocity, but its predictable. This is key.

So in a horizontal position, the frictional force depends on the negative force/acceleration generated by the weight times the coeffiecient of friction. Any help?

 

[m2003]

RESPONSE:

Hello, as a scientist, I understand your confusion regarding the problem. Let me help you understand the concept of frictional forces and 1D motion and how to approach this problem.

Firstly, frictional forces are a type of force that opposes motion between two surfaces in contact. In this problem, the rubber tire and wet concrete road are in contact, and the coefficient of kinetic friction (0.5) tells us how much force is needed to keep the tire in motion. This means that the force of friction between the tire and road is 0.5 times the weight of the car.

Now, to solve for the minimum time it will take for the car to come to a stop, we can use the equation: Vf = Vi + at, where Vf is the final velocity (0 mi/hr in this case), Vi is the initial velocity (30 mi/hr), a is the acceleration (which we can find using the coefficient of friction and the weight of the car), and t is the time we are looking for.

To find the acceleration, we can use the equation: Ff = μmg, where Ff is the force of friction, μ is the coefficient of friction, m is the mass of the car, and g is the acceleration due to gravity (9.8 m/s^2). Rearranging this equation, we get: a = μg.

Substituting this value of acceleration in the first equation, we get: 0 = 30 mi/hr + (μg)t. Solving for t, we get t = -30 mi/hr / (μg). Since the time cannot be negative, we take the absolute value of this expression, giving us the minimum time it will take for the car to come to a stop.

To find the distance the car will cover in this time, we can use the equation: d = Vit + 1/2at^2, where d is the distance, Vi is the initial velocity, t is the time we just calculated, and a is the acceleration. Substituting the values, we get: d = (30 mi/hr)(-30 mi/hr / (μg)) + 1/2(μg)(-30 mi/hr / (μg))^2. Simplifying this, we get d = 450 mi / g.

I hope this explanation helps you understand the problem better and how to approach it using the relevant equations