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 2.60 kg , up an incline of constant slope angle 30.0 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 6.00×102. 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.

Explanation / Answer

Work is given by:

W = Fk*s

Fk = umg*cos A

s = h/sin A

which gives

W = umgh/tan A

potential energy is given by:

U = -mgh

kinetic energy is given by:

KE = 0.5*mv^2

work energy theoram:

0.5*mv^2 = mgh + umgh/tan A

v = sqrt(2gh(1+u/tan A))

v = sqrt(2*9.81*3.4(1 + 0.06/tan 30))

v = sqrt(2*9.81*3.4(1 + 0.06*1.732)) = 8.581 m/sec

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.