Posted by **James** on Monday, May 27, 2013 at 12:29pm.

Starting from rest, a skier slides 100 m down a 28 degree slope.How much longer does the run take if the coefficient of kinetic friction is 0.17 instead of 0?

- Physics -
**MathMate**, Monday, May 27, 2013 at 6:40pm
Case 1: zero friction

F=mg sin(28)

a=F/m=g sin(28)

S=ut+(1/2)at²

100=0+g sin(28)t²/2

t=sqrt(2*100/(g sin(28))

=6.59 s.

Case 2: μ_{k}=0.17

Frictional force

=μmg cos(28)

Net force (assuming μcos<sin)

=mg(sin(28)-μcos(28)

t=sqrt(2*100/(g (sin(28)-μcos(28))

=7.99 s

Take the difference.

- Physics -
**Frank**, Monday, October 10, 2016 at 1:55am
shouldn't case 1 be cos(28) lol

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