You are a member of an alpine rescue team and must get a box of supplies, with m
ID: 2060391 • Letter: Y
Question
You are a member of an alpine rescue team and must get a box of supplies, with mass 2.10 kg, up an incline of constant slope angle 30.0 degree so that it reaches a stranded skier who is a vertical distance 3.00 m 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 9.81 m/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.
v = ________ m/s
Explanation / Answer
Law of conservation of energy final energy is energy lost + potential energy, since there does not need to be kinetic energy, and you don't want kintic energy, at the final position. PE = mgh = (2.10)(9.81)(3.00) = 61.8 J E lost = Ffd = FNud = mgcos30ud = (2.10)(9.81)cos30(6.00x10^-2)(3/sin30) = 6.42 J total Ef = 61.8 + 6.42 = 68.2 J Ei is completely kinetic energy as there is no relative potential energy and no energy is lost yet Ei=Ef, so Ek must equal 68.2 J Ek = (1/2)mv^2 = 68.2 J mv^2 = 136.5 v^2 = 65.0 v = 8.06 m/s Hope it helps :D
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