You are a member of an alpine rescue team and must get a box of supplies, with m
ID: 1969210 • Letter: Y
Question
You are a member of an alpine rescue team and must get a box of supplies, with mass 2.10kg , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 2.90m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10-2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81m/s^2 .Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.
Express your answer numerically, in meters per second.
Explanation / Answer
W = Fd = (µmgcos?+mgsin?)(h/sin?) = mgh (1 + (µ/tan?)) KE = ½mv² Work done = KE mgh (1 + (µ/tan?)) = ½mv² v = sqrt[2gh (1 + (µ/tan?))] = 7.92 m/s
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