(a)
The points where object is in equilibrium.
(a)
Explanation of Solution
Given:
The potential energy function is
The potential energy function is
Formula used:
Write the expression for force in terms of potential energy.
Here,
Calculation:
For
Substitute
Calculate the equilibrium points.
For
Substitute
Object would be in neutral equilibrium for
Conclusion:
Thus, object is in equilibrium at
(b)
The graph for
(b)
Explanation of Solution
Given:
The potential energy function is
The potential energy function is
Formula used:
The energy contained in an object due to its position when compared to other objects is called potential energy.
Write the expression of potential energy for
Here,
Write the expression of potential energy for
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
The graph for
Conclusion:
Thus, the graph for
(c)
The stable and unstable points of equilibrium.
(c)
Explanation of Solution
Given:
The potential energy function is
The potential energy function is
Formula used:
Write the expression for force in terms of potential energy.
Here,
Calculation:
For
Substitute
Calculate the equilibrium points.
For
Substitute
Object would be in neutral equilibrium for
Calculate the potential energy at all equilibrium points.
For
For
Conclusion:
The value of potential energy is maximum at
(d)
The speed of object at
(d)
Explanation of Solution
Given:
The potential energy function is
The potential energy function is
The mass of object is
The total energy of object is
Formula used:
Write the expression for potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Write the expression of total energy.
Here,
Substitute
Calculation:
Substitute
Substitute
Conclusion:
The speed of object at
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Chapter 7 Solutions
Physics for Scientists and Engineers
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