You are a member of an alpine rescue team and must get a box of supplies, with m
ID: 1550976 • Letter: Y
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 2.80 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. Express your answer numerically, in meters per second.
Explanation / Answer
The height of the skier is 2.8 m that means the potential energy of the box at the skier = mgh
= 3*9.81*2.8 = 82.404 J
Energy required to overcome friction = friction force*distance
= (us*mg)*(2.8/sin30) = (0.06*3*9.81)*(2.8/Sin30) = 9.89 J
Now applying the work energy theorem
Initial energy = Final energy
Kinetic energy - friction energy = Potential energy
Kinetic energy = 82.404 + 9.89 = 92.2925 J
(1/2)mV2 = 92.2925
V = 7.8439 m/s
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