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^{circ} so that it reaches a stranded skier who is a vertical distance 3.40 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.

Explanation / Answer

Applying work energy theorem, -1/2 * m * v^2 + mgh = -µmgcos30 => v^2 = 2*0.06*9.81*cos30 + 2*9.81* => v = 4.54 m/s

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