Concept explainers
(a)
The velocity of pan just after the landing of oranges.
(a)
Answer to Problem 112P
The velocity is
Explanation of Solution
The spring constant is
Write the equation for law of conservation of energy for the fall of oranges.
Here,
Rewrite the above equation in terms of
Write the equation for law of conservation of momentum for before and after the landing of oranges on pan.
Here,
Conclusion:
Substitute
Substitute
Therefore, the velocity is
(b)
The new equilibrium point of pan with oranges from the position before the oranges was dropped.
(b)
Answer to Problem 112P
The distance to new equilibrium point is
Explanation of Solution
The spring constant is
Write the equilibrium condition for the old equilibrium point.
Here,
Write the equation for new equilibrium on adding certain amount of mass.
Here,
Conclusion:
Substitute
Therefore, the distance to new equilibrium point is
(c)
The amplitude of the oscillations.
(c)
Answer to Problem 112P
The amplitude is
Explanation of Solution
The spring constant is
Write the equation for law of conservation of energy.
Here,
Write the equation for
Write the equation for
Write the equation for
Rewrite equation (I) by substituting equations (II), (III), (IV) and
Eliminate the common terms and rewrite the above expression in terms of
Conclusion:
Substitute
Therefore, the amplitude is
(d)
The frequency of oscillations of the system.
(d)
Answer to Problem 112P
The frequency is
Explanation of Solution
The spring constant is
Write the equation for the oscillations of a spring.
Here,
Conclusion:
Substitute
Therefore, the frequency is
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