How Long Can the Climber Hang Before the Rock Falls?

[pediepit]

Homework Statement

A 65 kg climber finds himself dangling over the edge of an ice cliff, as shown in the figure below. Fortunately, he's roped to a 940 kg rock located 51 m from the edge of the cliff. Assume that the coefficient of kinetic friction between rock and ice is 5.7×10−2. What is his acceleration, and how much time does he have before the rock goes over the edge? Neglect the rope's mass.

Homework Equations

Rock
F_T - F_f = mass_rock * a
N = mass_rock * g

Climber
F_T - mass_climber * g = mass_climber * a

The Attempt at a Solution

I solved for F_T for the climber and then stuck this equation into F_T in the rock equation. Then solved for a.

a = (g(mass_climber - Mu(k) * mass_rock)) / (mass_rock - mass_climber)

Plugging the numbers in the equation, i get a = 0.127904 m/s² My homework tells me this is wrong and I can't figure out why. any help is appreciated!

 

[ƒ(x)]

What's the force of friction?

What is the books answer btw?

 

[pediepit]

F_f = Mu(k) * N or Mu(k) * mass_rock * g

it's actually homework on the computer and doesn't give me the answer. Just tells me mine is wrong and to try again!

 

[pediepit]

figured it out

FT - mass_climber * g = mass_climber * a
should be
FT - mass_climber * g = -mass_climber * a
since the climber is moving downward