You are a member of an alpine rescue team and must get a box of supplies, with m
ID: 2280890 • Letter: Y
Question
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 so that it reaches a stranded skier who is a vertical distance 3.50m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00Ý102. 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/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.
I keep getting 8.91 m/s but it says that's wrong?
Explanation / Answer
final total energy = P.E. + K.E.
K.E. = 0 because velocity = 0 ( k.e. = .5 m v^2)
T.E. = mgh + 0 = (3)(9.81)(3.5) = 103.005
innitial t.e. = p.e. + k.e. = 0 + 0.5 (3)v^2
total energy is conserved
.5(3)(v^2) = (3)(9.81)(3.5)+ work done by friction. --- (1)
work done by friction = frictional force * distance = coeff of friction *m*g *d = 6x10^-2*3*9.81*3.5/cos30
plug this in equation 1 and solve for v
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.