How Long Can the Climber Hang Before the Rock Falls?

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Homework Help Overview

The problem involves a climber and a rock, focusing on the dynamics of the climber's descent and the forces acting on both the climber and the rock. The subject area includes mechanics, specifically forces, acceleration, and friction.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the acceleration of the climber and the time before the rock falls, using equations related to forces and friction. Some participants question the calculations and the setup of the equations, particularly regarding the direction of acceleration.

Discussion Status

Participants are actively discussing the equations used and the assumptions made in the problem. There is an indication that some guidance has been provided regarding the correct formulation of the equations, particularly in relation to the direction of forces acting on the climber.

Contextual Notes

The problem involves specific numerical values and constraints, such as the masses of the climber and the rock, the distance from the edge of the cliff, and the coefficient of kinetic friction. The homework context suggests that the solution must be derived without direct answers provided by the system.

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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
FT - Ff = massrock * a
N = massrock * g

Climber
FT - massclimber * g = massclimber * a

The Attempt at a Solution



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

a = (g(massclimber - Mu(k) * massrock)) / (massrock - massclimber)

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!
 
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What's the force of friction?

What is the books answer btw?
 
Ff = Mu(k) * N or Mu(k) * massrock * 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!
 
figured it out

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

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