- #1
murrskeez
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Homework Statement
A truck is traveling at 11.1 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 15.0° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.750. How far does the truck travel before coming to a stop? Use energy to solve this problem.
Homework Equations
fk = Ef - Ei
fk = μk*FN
FN=mgcos15°
The Attempt at a Solution
First, I found the work done by the friction force: Wfk = S(μkFN)cos180°
Wfk = μk(mgcos15°)(-1)
Then I solved for the work done by friction using the energy equation:
W = 1/2(mv2) +mgy - 1/2(mvi2) -mgyi
W = 0 + mgy - 1/2(mvi2) - 0
then I set the two equations equal to one another:
μk(mgcos15°)(-1) = mgy - 1/2(mvi2)
the m's canceled out and I solved for y:
y = μk(gcos15°)(-1) + 1/2(vi2) / g
and plugged in values:
y = (0.750)(9.8m/s2)(cos15°)(-1) + 1/2(11.0)2 / 9.8m/s2
and got: y = 6.90 m
knowing that the truck was traveling at 15°, sin15° = y/s
s = 6.90/sin15°
s = 26.7m
the correct answer should be 13.5m. Any help/advice would be much appreciated.