You are a member of an alpine rescue team and must project a box of supplies, wi
ID: 1693757 • Letter: Y
Question
You are a member of an alpine rescue team and must project a box of supplies, with mass m, up an incline of constant slope angle lpha 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 mu_mathrm{k}. 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.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 in terms of some or all of the variables m, g, h, mu_k, and alpha.
Explanation / Answer
Let v be the minimum velocity required to the skier. Angle of inclination = a Coefficient of Kinetic friction = µ From triangle law we can write Distance to be covered by the mass = Length of the slope of inclined plane S = h/sina -----------(1) Minimum force to be applied F = mg sina + friction = mg sina + µ mg cosa = mg ( sina + µ cosa) ------------(2) According to work energy theorem Work done = Change in Kinetic energy F S = (1/2)mv^2 - 0 mg ( sina + µ cosa)(h/sina) = (1/2)mv^2 (from (1) & (2)) mgh(1 + µ cota) = (1/2)mv^2 v^2 = 2gh[1 + µ cota] v = Sqrt(2gh[1 + µ cota])Related Questions
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