A uniform ladder with mass m2 = 14kg and length L = 3.2m rests against a smooth wall. A do-it-yourself enthusiastof mass mi = 70kg stands on the ladder a distance d=1.2m from the bottom (measured along the ladder.) There isno friction between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and theladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and Nz is the magnitude of thenormal force exerted by the ground on the ladder.What angle 0, will cause the static friction with the floor to be maximized? Will the ladder start to slip when theangle is made larger, or smaller than this borderline value?1) Draw a free body diagram for the ladder, choose a coordinate system and write out the equations forthe sum of the x forces and the sum of the y forces.2) Draw a diagram of the ladder with each force vector acting on it at its point of application. Chose anaxis of rotation and place this on the diagram as well. (Note: Any choice will work, you just have to beconsistent later.)3) Find the length of the lever arm for each force acting on the ladder, and also list whether that forcewould tend to cause clockwise or counter-clockwise rotation.4) Write out the net torque equation for the ladder.5) Setting the static friction to maximum, use algebra to solve the pair of equations in 1 and 4 for theangle of the ladder.

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A uniform ladder with mass m; = 14kg and length L= 3.2m rests against a smooth wall. A do-it-yourself enthusiast of mass m = 70kg stands on the ladder a distance d= 1.2m from the bottom (measured along the ladder.) There is no frietion between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and the ladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and N; is the magnitude of the normal force exerted by the ground on the ladder. What angle e, will cause the static friction with the floor to be maximized? Will the ladder start to slip when the angle is made larger, or smaller than this borderline value?

A uniform ladder with mass m; = 14kg and length L= 3.2m rests against a smooth wall. A do-it-yourself enthusiast of mass m = 70kg stands on the ladder a distance d= 1.2m from the bottom (measured along the ladder.) There is no frietion between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and the ladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and N; is the magnitude of the normal force exerted by the ground on the ladder. What angle e, will cause the static friction with the floor to be maximized? Will the ladder start to slip when the angle is made larger, or smaller than this borderline value?

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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