Concept explainers
(a)
The total energy of the oscillating system.
(a)
Answer to Problem 27P
The total energy of the oscillating system is
Explanation of Solution
Given that the force constant of the spring is
Write the expression for the energy of the spring-object oscillating system.
Here,
Conclusion:
Substitute
Therefore, the total energy of the oscillating system is
(b)
The speed of the object when its position is
(b)
Answer to Problem 27P
The speed of the object when its position is
Explanation of Solution
Given that the force constant of the spring is
Write the expression for the speed at a given position of an object executing
Here,
Write the expression for the angular frequency of the spring-object system.
Use equation (III) in (II).
Conclusion:
Substitute
Therefore, the speed of the object when its position is
(c)
The kinetic energy of the object when its position is
(c)
Answer to Problem 27P
The kinetic energy of the object when its position is
Explanation of Solution
Write the expression for the kinetic energy of the oscillating object.
Here,
Equation (I) gives the total energy of the system.
Write the expression for the potential energy of the object at the given position.
Use equation (I) and (VI) in (V).
Conclusion:
Substitute
Therefore, the kinetic energy of the object when its position is
(d)
The potential energy of the object when its position is
(d)
Answer to Problem 27P
The potential energy of the object when its position is
Explanation of Solution
It is obtained that the total energy of the system is
Write the expression for the potential energy of the object.
Conclusion:
Substitute
Therefore, the potential energy of the object when its position is
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Chapter 15 Solutions
PHYSICS:F/SCI...W/MOD..-UPD(LL)W/ACCES
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