Concept explainers
(a)
The condition that determines
(a)
Answer to Problem 5.1P
The net force acting on the spring is
Explanation of Solution
The stretched length of the spring
The net force acting on the spring when the mass is attached to it and it is in equilibrium position is zero because the downward pull of gravity on the mass is counter equally by the spring force in opposite direction.
Here, m is the mass, g is the acceleration due to gravity, and k is the spring constant.
Now, when the spring is pulled further down by a distance x beyond its new equilibrium position, then net force on the mass is,
Substitute 0 for
Conclusion:
Therefore, the net force acting on the spring is
(b)
To prove the net potential energy has the form
(b)
Answer to Problem 5.1P
The net potential energy has the form
Explanation of Solution
The stretching force is conservative as the net stretching force depends only on the distance the spring is stretched, that is x.
Write the expression for the potential energy.
Substitute
Conclusion:
Therefore, the net potential energy has the form
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Chapter 5 Solutions
Classical Mechanics
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