Car traveling on horizontal road with force of static friction

[Color_of_Cyan]

Homework Statement

A car is traveling at 50 mi / hr on a horizontal highway

a. If the coefficient of static friction between the road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?

b. What is the stopping distance when the surface is dry and μ_s = 0.600?

Homework Equations

∑ f = ma

f_s = (μ_s)(normal force)

Xf = Xi + (Vi)(t) + (1/2)at²

The Attempt at a Solution

Do not know where to start, please help.

Part a:

∑ Fx = ma - f_s = 0

f_s = (μ_s)(normal force)

∑ Fy = (normal force) = mg

ma = f_s therefore ma = (μ_s)(normal force)

a = (μ_s)(normal force) / mass

Now: vf = 0

vi = 73.3 ft / second

Xf = Xi + Vi t + (1/2)at²

0 = 50 mi / hr + [ (0.100)(normal force) / mass ][t²]

 

[PhanthomJay]

Homework Statement

A car is traveling at 50 mi / hr on a horizontal highway

a. If the coefficient of static friction between the road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?

b. What is the stopping distance when the surface is dry and μ_s = 0.600?

Homework Equations

∑ f = ma

f_s = (μ_s)(normal force)

Xf = Xi + (Vi)(t) + (1/2)at²

The Attempt at a Solution

Do not know where to start, please help.

Actually, you have started off pretty well.

Part a:

∑ Fx = ma - f_s = 0

Yes, but try to avoid the use of pseudo inertial forces, where practical, when using Newton's 2nd law. Rather use F_net = ma, where F_net in this case is f_s, in the direction of the acceleration. It's the same result as F_net = ma - f_s = 0, but it avoids confusion down the road.

f_s = (μ_s)(normal force)

∑ Fy = (normal force) = mg

ma = f_s therefore ma = (μ_s)(normal force)

a = (μ_s)(normal force) / mass

Now: vf = 0

vi = 73.3 ft / second

Xf = Xi + Vi t + (1/2)at²

0 = 50 mi / hr + [ (0.100)(normal force) / mass ][t²]

Rather than use this kinematic equation that relates distance, acceleration, initial velocity, and time, use the kinematic equation of motion that relates distance, initial and final velocity, and acceleration. That avoids solving for the time.

 

[Color_of_Cyan]

That helped a lot, thanks!

I didn't know you were supposed to set netforce equal to force of static friction.