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 2.30kg , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 2.90m 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 9.81m/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

Note that by conservation of energy,

Wncon = delta(KE) + delta(PE)

Here,

KEi = 1/2 m v^2
KEf = 0
delta PE = mgh
Wncon = -uk m g h / sin 30

Thus, solving for v,

v = 7.92 m/s [ANSWER]

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