Minimum distance in which the car will stop?

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SUMMARY

The problem involves calculating the minimum stopping distance of a car traveling at 51.0 mi/h on a horizontal highway with a static friction coefficient of 0.100. The relevant equations include Newton's second law, kinematic equations, and the friction equation. The solution does not require the car's mass, as it cancels out in the calculations. The focus should be on the relationship between friction, acceleration, and distance using the given parameters.

PREREQUISITES
  • Understanding of Newton's second law (ΣF = m a)
  • Familiarity with kinematic equations (v² = v₀² + 2 a Δx)
  • Knowledge of static friction and its equation (fₛ ≤ μₛ N)
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Calculate stopping distance using the formula Δx = (v²)/(2a) with a derived acceleration from friction.
  • Explore the impact of varying coefficients of friction on stopping distances.
  • Investigate the role of mass in dynamics and how it affects force calculations.
  • Study conservation of energy principles in the context of braking systems.
USEFUL FOR

Students in physics courses, automotive engineers, and anyone interested in understanding vehicle dynamics and stopping distances under varying conditions.

hm8
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Homework Statement


A car is traveling at 51.0 mi/h on a horizontal highway.
If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?

Homework Equations


<br /> \Sigma \vec{F} = m \vec{a}<br />

<br /> v^2 = v_0^2 + 2 a \Delta x<br />

<br /> f_s \leq \mu_s N<br />

The Attempt at a Solution


Is it possible to do this problem without mass? Or did my teacher just forget to give us the mass?

If I had the mass of the car, I'd use it to find the normal force, and then plug that into the friction equation to find the force of friction...and then plug that into Newtons 2nd to find acceleration, and then use kinematics to find distance.

I suppose the minimum distance would be 0 if the car's mass was infinite but...I don't think that's what he's looking for.
 
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masses should drop out at the very end. Are you allowed to use conservation of energy? If you can than its just as simple as knowing the work done by the road and brakes
 

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