1) what angle will the ladder make with the horizontal? 2) Now since she has car
ID: 1701084 • Letter: 1
Question
1) what angle will the ladder make with the horizontal?
2) Now since she has carefully lowered the ladder down to the botton, she isnt entirely sure if it will hold. Her mass is 48 kg. First we need to find the normal force due to vertical wall. What will it be? Assume the wall is frictionless.
3) Using normal force you just found, determine the force of friction between the ladder and horizontal surface compared it to the maximum allowed friction force between the ladder and horizontal surface. The coefficient of static friction is 0.75. Can she make it?
4) If yes, what will happen to the friction force as she climbs down the ladder? If no, would it make a difference if there was friction between the ladder and the vertical wall?
Explanation / Answer
1)
From the diagram cos = 2 m/3.8 m
= 58.240
2)
The mass of G is M = 48 kg
Let R be the normal reaction of the wall on the ladder
taking the torques in counter clockwise
mgcos*L/2 = Rcos(90-)*L
15*9.8*cos58.24 *1.9 = R*cos31.76*3.8
R = 45.5 N
3) The coefficient of friction = 0.75
The frictional force between the ladder and the horizontal surface is f = R = 45.5 N
The maximum allowed friction force between the ladder and the horizontal surface is
f(max) = mg
f(max) = 0.75*15*9.8
f(max) = 110.25 N
The frictional force between the ladder and the horizontal surface is f = 0.413*f(max)
Yes she can make it
4)
When she climbs down the ladder, the additional torque due to her will be compensated by the additional frictional force (max) sothat she can climb down safely
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.