Car traveling on horizontal road with force of static friction

Color_of_Cyan

1. 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 μs = 0.600?

2. Homework Equations
∑ f = ma

fs = (μs)(normal force)

Xf = Xi + (Vi)(t) + (1/2)at2

3. The Attempt at a Solution

Part a:

∑ Fx = ma - fs = 0

fs = (μs)(normal force)

∑ Fy = (normal force) = mg

ma = fs therefore ma = (μs)(normal force)

a = (μs)(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]

Related Introductory Physics Homework Help News on Phys.org

PhanthomJay

Homework Helper
Gold Member
1. 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 μs = 0.600?

2. Homework Equations
∑ f = ma

fs = (μs)(normal force)

Xf = Xi + (Vi)(t) + (1/2)at2

3. The Attempt at a Solution
Actually, you have started off pretty well.
Part a:

∑ Fx = ma - fs = 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 fs, in the direction of the acceleration. It's the same result as F_net = ma - fs = 0, but it avoids confusion down the road.
fs = (μs)(normal force)

∑ Fy = (normal force) = mg

ma = fs therefore ma = (μs)(normal force)

a = (μs)(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.

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