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 2.50 kg , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 3.30 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

here ,

mass , m = 2.5 kg

theta = 30 degree

height , h = 3.3 m

uk = 0.06

let the speed required be v

using work energy theorm

work done by friction force = kientic energy needed - potential energy at the top

uk * m * g *cos(theta) * (h /sin(theta)) = 0.5 * m * v^2 - m * g * h

0.06 * 9.8 * cos(30) * ( 3.3 /sin(30)) = 0.5 * v^2 - 9.8 * 3.3

v = 8.44 m/s

the initial speed at the bottom of the incline is 8.44 m/s

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