(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

f_{k}= E_{f}- E_{i}

f_{k}= μ_{k}*F_{N}

F_{N}=mgcos15°

3. The attempt at a solution

First, I found the work done by the friction force: W_{fk}= S(μ_{k}F_{N})cos180°

W_{fk}= μ_{k}(mgcos15°)(-1)

Then I solved for the work done by friction using the energy equation:

W = 1/2(mv^{2}) +mgy - 1/2(mv_{i}^{2}) -mgy_{i}

W = 0 + mgy - 1/2(mv_{i}^{2}) - 0

then I set the two equations equal to one another:

μk(mgcos15°)(-1) = mgy - 1/2(mv_{i}^{2})

the m's cancelled out and I solved for y:

y = μk(gcos15°)(-1) + 1/2(v_{i}^{2}) / g

and plugged in values:

y = (0.750)(9.8m/s^{2})(cos15°)(-1) + 1/2(11.0)^{2}/ 9.8m/s^{2}

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.

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# Homework Help: Using Energy to Solve Work Problem

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