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A 14.5-m uniform ladder weighing 485 N rests against a frictionless wall. The ladder makes a 63.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 845-N firefighter has climbed 3.74 m along the ladder from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 8.75 m from the bottom, what is the coefficient of static friction between ladder and ground?

A 14.5-m uniform ladder weighing 485 N rests against a frictionless wall. The ladder makes a 63.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 845-N firefighter has climbed 3.74 m along the ladder from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 8.75 m from the bottom, what is the coefficient of static friction between ladder and ground?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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12.1

A 14.5-m uniform ladder weighing 485 N rests against a frictionless wall. The ladder makes a 63.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 845-N firefighter has climbed 3.74 m along the ladder from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 8.75 m from the bottom, what is the coefficient of static friction between ladder and ground?
Transcribed Image Text:A 14.5-m uniform ladder weighing 485 N rests against a frictionless wall. The ladder makes a 63.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 845-N firefighter has climbed 3.74 m along the ladder from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 8.75 m from the bottom, what is the coefficient of static friction between ladder and ground?
(a) The wall is frictionless, but it does exert a horizontal normal force nw. For the x and y components of the force, we have the following from Newton's second law. Fx = fs - nw = 0 Fy = ng- 845 Taking torques about an axis at the foot of the ladder, we have the following. Στι τ = 0 nw = = 845 = ( 8 +(485 N)(0 The correct answer is not zero. m sin 27° - nw( n. 14.5 nw' = Solving this equation for [(3.74 m) The correct answer is not zero. m we have N 835 14.5 - 485 N = 0 N) (3.74 m) X 3.74 m sin 27° m cos 27° N+ 0 m) (485 N)] N. Next substitute the value for nw into the Fx equation to find W fs="w n N. The friction force is in the positive x direction toward the wall. m X tan 27°
Transcribed Image Text:(a) The wall is frictionless, but it does exert a horizontal normal force nw. For the x and y components of the force, we have the following from Newton's second law. Fx = fs - nw = 0 Fy = ng- 845 Taking torques about an axis at the foot of the ladder, we have the following. Στι τ = 0 nw = = 845 = ( 8 +(485 N)(0 The correct answer is not zero. m sin 27° - nw( n. 14.5 nw' = Solving this equation for [(3.74 m) The correct answer is not zero. m we have N 835 14.5 - 485 N = 0 N) (3.74 m) X 3.74 m sin 27° m cos 27° N+ 0 m) (485 N)] N. Next substitute the value for nw into the Fx equation to find W fs="w n N. The friction force is in the positive x direction toward the wall. m X tan 27°
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