You are a member of an Alpine Rescue Team. You must project a box of supplies up an incline of constant slope angle a so that it reaches a stranded skier who is a vertical distance h above the bottom of the incline. The incline is slippery, but there is some friction present, with kinetic friction coefficient µk. Use the work–energy theorem to calculate the minimum speed you must give the box at the bottom of the incline so that it will reach the skier. Express your answer in terms of g, h, µk, and ?.

Solution 21E Step 1: The diagram below shows the innards of the problem clearly. Step 2: The work energy theorem tells that, The difference between final and initial kinetic energy is the work done. So, K.E final K.E initialW 0 1/2 mv = work done by gravity + work done by friction. 1/2 mv = W + W ---------------------(1) G F So, let’s calculate the work done by the gravitational force first. Step 3: Here the angle between the gravitational force and the displacement of the box is 90 degree. So, the work done will be, W = F . d = F d cos (90 + ) G G G = mgd × ( sin ) = mgd sin ------------------------(2)