Concept explainers
(a)
An algebraic solution for
(a)
Answer to Problem 125P
An algebraic solution for
Explanation of Solution
The system is in equilibrium until the ladder begins to slip.
Write the expression for the Newton’s second law for the equilibrium.
Here,
Write the expression for
Here,
Put the above equation in equation (I).
The frictional force has its maximum possible magnitude at the person’s highest point.
Write the equation for the maximum possible magnitude of frictional force.
Here,
Put the above equation in equation (II).
The net external force on the system in the
Here,
Write the expression for
Here,
Put the above equation in equation (IV) and rewrite it for
Put the above equation in equation (III).
Choose the axis of rotation at the contact point between the ladder and the floor.
The net torque about the rotation axis is zero in equilibrium.
Here,
Write the expression for
Here,
Put the above equation in equation (VI) and rewrite it for
Put equation (V) in the above equation.
Conclusion:
Therefore, the algebraic solution for
(b)
Use the expression derived in part (a) to show that placing the ladder at a larger angle
(b)
Answer to Problem 125P
It is shown using the expression derived in part (a) that placing the ladder at a larger angle
Explanation of Solution
Refer to equation (VII) derived in part (a).
The value of
Conclusion:
Thus, it is shown using the expression derived in part (a) that placing the ladder at a larger angle
(c)
The maximum angle that enables the person to climb all the way to the top of the ladder.
(c)
Answer to Problem 125P
The maximum angle that enables the person to climb all the way to the top of the ladder is
Explanation of Solution
To climb up to the top of the ladder, set the value of
Put the above equation in equation (VII).
Rewrite the above equation for
Conclusion:
Given that the value of
Substitute
Therefore, the maximum angle that enables the person to climb all the way to the top of the ladder is
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