You are a member of an alpine rescue team and must get a box of supplies, with m
ID: 1697917 • Letter: Y
Question
You are a member of an alpine rescue team and must get a box of supplies, with mass 2.40 kg, up an incline of constant slope angle 30.0 degrees so that it reaches a stranded skier who is a vertical distance 3.20 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/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. (In units of m/s)
Explanation / Answer
KE0+PE0 = KEf+PEf+Wf Wf = work done by friction which equals Ff (Force of friction) times X (distance) X = 3.20/cos(30deg) = 6.4m N = mgcos(theta) = 2.40(9.81)(cos(30)) = 20.4N Ff = N(coefficient of kinetic friction) = 20.4(6.00x10^-2) = 1.224N PE0 = zero and KEf = zero 1/2m((v0)^2) = mgh+Ff(X) 1/2(2.40)((v0)^2) = 2.40(9.81)(3.20) + 1.224(6.4) v0 = 8.32m/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.