Concept explainers
(a)
Find the angular acceleration of the ladder.
(a)
Answer to Problem 16.119P
The angular acceleration of the ladder is
Explanation of Solution
Given information:
The weight of the ladder is
The length of the ladder is
The coefficient of kinetic friction is
The angle is
Calculation:
Consider the acceleration due to gravity
Calculate the mass of the ladder
Substitute
Calculate the moment of inertia
Substitute
Sketch the geometry of the ladder rests on the wall as shown in Figure 1.
Refer to Figure 1.
Calculate the distance
Substitute
Calculate the distance
Substitute
Sketch the Free Body Diagram of the ladder as shown in Figure 2.
Refer to Figure 2.
Apply the Equations of Equilibrium as shown below.
Apply the Equilibrium of force along x direction as shown below.
Apply the Equilibrium of force along y direction as shown below.
Apply the Equilibrium of moment about G as shown below.
Apply the kinematics as shown below.
Calculate the acceleration
Substitute
Calculate the acceleration
Substitute
Resolving the components of i and j in Equation (5) as shown below.
Calculate the acceleration
Substitute
Hence,
Calculate the reaction
Substitute
Calculate the reaction
Substitute
Calculate the reaction
Substitute
Calculate the angular acceleration
Substitute
Substitute
Hence, the angular acceleration of the ladder is
(b)
Find the forces at A and B
(b)
Answer to Problem 16.119P
The force at A is
The force at B is
Explanation of Solution
Given information:
The weight of the ladder is
The length of the ladder is
The coefficient of kinetic friction is
The angle is
Calculation:
Refer to part (a).
The angular acceleration of the ladder is
Calculate the reaction
Substitute
Calculate the force at A
Substitute
Hence, the force at A is
Calculate the reaction
Substitute
Calculate the force at B
Substitute
Therefore, the force at B is
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Chapter 16 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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