# A 154 kg bear runs up a hill that has a slope of 15 degrees to the horizontal.  The bear travels 1200m in 125 seconds. What is the work done by the bear?

justaguide | College Teacher | (Level 2) Distinguished Educator

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The bear runs up a hill that has a slope of 15 degrees to the horizontal. The mass of the bear is 154 kg and the distance traveled by the bear is 1200 m. The forces acting on the bear as it runs up the hill include the gravitational force of attraction of the Earth and a force of friction. To calculate the work done by the bear only the conservative forces are being considered here which allows the force of friction to be ignored.

As the bear runs up the hill, only the increase in the vertical height needs to be considered as the horizontal component is perpendicular to the gravitational force of attraction. Work is the dot product of force and displacement. As cos 0 = 1 and cos 90 = 0, only the increase in the vertical component needs to be considered to calculate the work done. The work done is 154*1200*sin 15 = 47829.75 J. As the bear does this work in 125 s, the power expended is 382.6 W.

The work done by the bear is 47.82975 kJ.

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