
Concept explainers
(a)
The length of the spring.
(a)

Answer to Problem 45PQ
The length of the spring is
Explanation of Solution
Following figure gives rod and spring system.
Following figure is the free body diagram of rod and spring system.
Write the expression for the horizontal distance between one end to other end of the spring.
Here,
Write the expression for
Here,
Write the expression for the vertical distance of the end of the spring from ground.
Here,
Write the expression for the length of the spring using Pythagoras theorem.
Here,
Conclusion:
Substitute
Substitute
This distance is also equal to vertical distance of the end of the spring from ground.
Substitute
Substitute
Therefore, the length of the spring is
(b)
The weight of the bar.
(b)

Answer to Problem 45PQ
The weight of the bar is
Explanation of Solution
At equilibrium, the net torque acting on the bar around the bottom pivot must be zero.
Write the expression for the torque about pivot in the rod due to gravity.
Here,
The direction of torque is into the page.
Using figure2, write the expression for the perpendicular distance between pivot of the rod and point where weight acts.
Write the expression for the radial vector from the pivot point to the end of the bar where the spring acts.
Here,
Write the expression for the relaxed length.
Here,
The magnitude of spring force depends on the extension relative to the relaxed spring length.
Write the expression for the magnitude of spring force.
Here,
Write the expression for the extension of spring relative to the relaxed spring length.
From figure2, write the expression for the angle spring force makes below the horizontal.
Here,
Write the expression for the spring force as a vector.
Here,
Write the expression for the torque on the rod due to spring force.
Here,
The direction of above torque is out of the page.
At equilibrium torque due to spring force and weight will cancel each other. Since, the directions of torques are opposite, their magnitude should be equal.
Write the equilibrium condition of the torques.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Use equations (XV) and (XVI) in (XIII) to get
Substitute
Therefore, The weight of the bar is
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Chapter 14 Solutions
Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term
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