   Chapter 13, Problem 40P

Chapter
Section
Textbook Problem

A simple pendulum is 5.00 in long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2?

(a)

To determine
The period of the simple harmonic motion of the pendulum which is in an elevator.

Explanation

Given info: The length of the pendulum is 5.00m . The elevator is accelerating upward at 5.00ms-2 .

The free body diagram of the pendulum,

From the figure,

Tmg=ma (1)

• T is the tension on the string
• m is the mass of the object
• g is the free fall acceleration
• a is the acceleration of the elevator

From (1)

T=m(g+a)=mgapparent

• gapparent is the apparent free fall acceleration

Choose the downward direction to be the positive direction. Apparent free fall acceleration of the pendulum in the elevator is,

gapparent=g+a=9.80ms-2+5.00ms-2=14

(b)

To determine
The period of the simple harmonic motion of the pendulum this is in an elevator.

(c)

To determine
The period of a simple pendulum this is in an accelerating truck.

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