stopping distance- physics?

Question

(a) If the coefficient of kinetic friction between tires and dry pavement is µk, what is the shortest distance in which an automobile can be stopped by locking the brakes when traveling at v?
Take the free fall acceleration to be g.

(b) On wet pavement the coefficient of kinetic friction may be only µ_wet . How fast should you drive on wet pavement in order to be able to stop in the same distance as in part (a)?

Answer 1

You can solve this using energy conservation since the brakes are locked. FYI: If the brakes were not locked, then the energy would be converted to heat energy on the brakes as long as the wheels don't skid.


For the scenario described in the problem:
The car has .5*m*v^2 kinetic energy

The force of friction is µk*m*g
it does work over the stopping distance,d
so
.5*m*v^2=µk*m*g*d
d=.5*v^2/(µk*g)

in part b
use v'
d=.5*v'^2/(µ_wet *g)
since the d is the same
v^2/µk=v'^2/µ_wet
v'=sqrt(v^2*µ_wet/µk)

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