Chapter 6: Q. 92 (page 366)

A pendulum swings through an angle of $20^{\circ}$ each second. If the pendulum is $40$ inches long, how far does its tip move each second? Round answers to two decimal places.

Short Answer

Expert verified

The tip of the pendulum moves $13.96$ inches each second.

Step by step solution

Step 1. Given information

Given, a $40$ inches long pendulum swings $20^{\circ}$ in each second.

We consider the movement of a pendulum as a circular motion object.

Step 2. Used formulae

We use the formula $S = r θ$ to obtain the arc length of a circle, where $r$ is the radius and $θ$ is the angle made by the arc.

Step 3. Conversion of Angles

Given angle $20^{\circ}$ , when converted to radians, it becomes, $θ = 20 \cdot \frac{π}{180} = \frac{π}{9}$

Step 4. Calculation

Substituting the values and using the formulae,

$s = 40 \cdot \frac{π}{9} \approx 13.96$ inches.

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A pendulum swings through an angle of $20^{\circ}$ each second. If the pendulum is $40$ inches long, how far does its tip move each second? Round answers to two decimal places.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Used formulae

Step 3. Conversion of Angles

Step 4. Calculation

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A pendulum swings through an angle of 20∘ each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Used formulae

Step 3. Conversion of Angles

Step 4. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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A pendulum swings through an angle of $20^{\circ}$ each second. If the pendulum is $40$ inches long, how far does its tip move each second? Round answers to two decimal places.