You are a member of an alpine rescue team and must get a box of supplies, with m

Question

You are a member of an alpine rescue team and must get a box of supplies, with mass 2.20 , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 3.50 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 .
Use the work-energy theorem to calculate the minimum speed that you must give the box at the bottom of the incline so that it will reach the skier.

Explanation / Answer

The distance you need to move the box is: L = H/sin(30°) = 6.2 m Coeffient of friction, µ = 6x10^-2 To push the box up to the skier, you must over friction and gravity along the incline: KE = (F(friction) + mgcos(30°))L = ½mv² (µN - mgcos(30°))L = ½mv² (µmgsin(30°) - mgcos(30°))L = ½mv² v = sqrt(2L(µgsin(30°) - gcos(30°)))

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