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A simple pendulum is 5.00 m long. What is the period of small oscillations for this pendulum in the following situations?

(a) The pendulum is located in an elevator accelerating upward at [tex]5.00 \, \text{m/s}^2[/tex].

(b) The pendulum is located in an elevator accelerating downward at [tex]5.00 \, \text{m/s}^2[/tex].

(c) The pendulum is placed in a truck that is accelerating horizontally at [tex]5.00 \, \text{m/s}^2[/tex].

Answer :

Final answer:

The period of a simple pendulum depends on its length and the acceleration due to gravity. It is affected by the acceleration of the elevator in an upward or downward direction. However, the period is not affected by the horizontal acceleration of the truck.

Explanation:

The period of a simple pendulum depends on its length and the acceleration due to gravity. The period is completely independent of other factors, such as mass and the maximum displacement. In an elevator accelerating upward at 5.00 m/s², the effective acceleration acting on the pendulum will be the sum of the acceleration due to gravity and the acceleration of the elevator. The effective acceleration will be greater than g, and therefore the period will be shorter.

In an elevator accelerating downward at 5.00 m/s², the effective acceleration acting on the pendulum will be the difference between the acceleration due to gravity and the acceleration of the elevator. The effective acceleration will be less than g, and therefore the period will be longer.

In a truck accelerating horizontally at 5.00 m/s², the acceleration of the truck does not affect the period of the pendulum. The period will remain the same as in a stationary location.

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