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 3.00 kg , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 2.90 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×102. 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/s2 . 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.

Explanation / Answer

d = 2.9/sin30° = 5.8 m

Ff = µ*mg*cos30° = 1.529 N

Ef = Ff*d = 8.868 J

½mv² = mgy + 8.868

v = (2g*2.9 +8.868) =8.10 m/s

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