Delivering Rescue Supplies You are a member of an alpine rescue team and must ge

Question

Delivering Rescue Supplies You are a member of an alpine rescue team and must get a box of supplies, with mass 3.00kg , up an incline of constant slope angle 30.0 Degree so that it reaches a stranded skier who is a vertical distance 3.40m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00 x 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/s^2 .

Explanation / Answer

given,

mass of box = 3 kg

sliding distance box has to cover = 3.4 / sin(30)

sliding distance box has to cover = 6.8 m

frictional force = coefficient of friction * mass * g * cos(30)

frictional force = 6 * 10^-2 * 3 * 9.8 * cos(30)

frictional force = 1.52767 N

work done by frictional force = frictional force * distance

work done by frictional force = 1.52767 * 6.8

work done by frictional force = 10.388 J

kinetic energy = 0.5 * m * V^2

potential energy = m * g * h

potential energy = 3 * 9.8 * 3.4

potential energy = 99.96 J

by conservation of energy

initial energy = final energy

KE = frictional work + PE

0.5 * 3 * V^2 = 10.388 + 99.96

V = 8.577 m/s

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