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A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure.   Since the floor is rough, it exerts both a normal force  N1  and a frictional force  f1  on the ladder. However, since the wall is frictionless, it exerts only a normal force  N2  on the ladder. The ladder has a length of  L = 4.1 m,  a weight of  WL = 61.0 N,  and rests against the wall a distance  d = 3.75 m  above the floor. If a person with a mass of  m = 90 kg  is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 =  N N2 =  N f1 =  N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 =  N N2 =  N f1 =  N

A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure.   Since the floor is rough, it exerts both a normal force  N1  and a frictional force  f1  on the ladder. However, since the wall is frictionless, it exerts only a normal force  N2  on the ladder. The ladder has a length of  L = 4.1 m,  a weight of  WL = 61.0 N,  and rests against the wall a distance  d = 3.75 m  above the floor. If a person with a mass of  m = 90 kg  is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 =  N N2 =  N f1 =  N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 =  N N2 =  N f1 =  N

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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A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure.

 

Since the floor is rough, it exerts both a normal force 

N1

 and a frictional force 

f1

 on the ladder. However, since the wall is frictionless, it exerts only a normal force 

N2

 on the ladder. The ladder has a length of 

L = 4.1 m,

 a weight of 

WL = 61.0 N,

 and rests against the wall a distance 

d = 3.75 m

 above the floor. If a person with a mass of 

m = 90 kg

 is standing on the ladder, determine the following.

(a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.)
N1 =  N
N2 =  N
f1 =  N

(b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.)
N1 =  N
N2 =  N
f1 =  N
### Analyzing the Forces on a Ladder In this diagram, a person is standing on a ladder leaning against a vertical wall. The forces acting on the ladder and their directions are depicted in detail. #### Components of the Diagram: - **Person and Ladder**: The person is positioned near the top of the ladder, illustrating a typical scenario of someone using a ladder to reach an elevated position. - **Forces on the Ladder**: - \( mg \): The gravitational force acting downward, representing the combined weight of the person and the ladder (where \( m \) is the mass and \( g \) is the acceleration due to gravity). - \( N_1 \): The normal force exerted by the ground on the ladder, acting vertically upwards. - \( N_2 \): The normal force exerted by the wall on the ladder, acting horizontally to the left. - \( f_1 \): The frictional force at the base of the ladder, directed horizontally to the right, preventing the ladder from slipping. #### Coordinates and Distances: - **Axes**: - The \( x \)-axis is horizontal, and the \( y \)-axis is vertical, forming a standard Cartesian coordinate system. - **Measurements**: - \( b \): The horizontal distance from the base of the ladder to the wall. - \( d \): The vertical height from the ground to the point where the ladder contacts the wall. This diagram serves as a physical representation for understanding static equilibrium, focusing on the balance of forces acting on the ladder. It exemplifies the importance of each force in maintaining stability and preventing the ladder from sliding or toppling.
Transcribed Image Text:### Analyzing the Forces on a Ladder In this diagram, a person is standing on a ladder leaning against a vertical wall. The forces acting on the ladder and their directions are depicted in detail. #### Components of the Diagram: - **Person and Ladder**: The person is positioned near the top of the ladder, illustrating a typical scenario of someone using a ladder to reach an elevated position. - **Forces on the Ladder**: - \( mg \): The gravitational force acting downward, representing the combined weight of the person and the ladder (where \( m \) is the mass and \( g \) is the acceleration due to gravity). - \( N_1 \): The normal force exerted by the ground on the ladder, acting vertically upwards. - \( N_2 \): The normal force exerted by the wall on the ladder, acting horizontally to the left. - \( f_1 \): The frictional force at the base of the ladder, directed horizontally to the right, preventing the ladder from slipping. #### Coordinates and Distances: - **Axes**: - The \( x \)-axis is horizontal, and the \( y \)-axis is vertical, forming a standard Cartesian coordinate system. - **Measurements**: - \( b \): The horizontal distance from the base of the ladder to the wall. - \( d \): The vertical height from the ground to the point where the ladder contacts the wall. This diagram serves as a physical representation for understanding static equilibrium, focusing on the balance of forces acting on the ladder. It exemplifies the importance of each force in maintaining stability and preventing the ladder from sliding or toppling.
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