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 2.70 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.

v= ___ m/s

Explanation / Answer

Here

coefficient of kinetic friction , uk = 0.06

distance , d = 2.70 m

mass , m = 2.50 Kg

theta = 30 degree

Using conservation of energy

0.5 * m * v^2 = m * g * d * sin(theta) + uk * m * g * d * cos(theta)

0.5 * 2.5 * v^2 = 2.5 * 9.8 * 2.70 * sin(30) + 0.06 * 2.5 * 9.8 * 2.7 * cos(30)

solving for v

v = 5.405 m/s

the minimum speed of the box of incline at the bottom needed is 5.405 m/s

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