=103. Uses of the Pendulum.=--The chief use of the pendulum is to regulate motion in clocks. The wheels are kept in motion by a spring or a weight and the regulation is effected by an escapement (Fig. 82). At each vibration of the pendulum one tooth of the wheel _D_ slips past the prong at one end of the escapement _C_, at the same time giving a slight push to the escapement. This push transmitted to the pendulum keeps it in motion. In this way, the motion of the wheel work and the hands is controlled. Another use of the pendulum is in finding the acceleration of gravity, by using the formula, _t_ = π√(_l_/_g_), in which _t_ is the time in seconds of a single vibration and _l_ the length of the pendulum. If, for example, the length of the seconds pendulum is 99.31 cm., then 1 = π√(99.31/_g_); squaring both sides of the equation, we have 1² = π²(99.31/_g_), or _g_ = π² × 99.31/1² = 980.1 cm. per sec., per sec. From this it follows that, since the force of gravity depends upon the distance from the center of the earth, the pendulum may be used to determine the elevation of a place above sea level and also the shape of the earth. Important Topics 1. Simple pendulum. 2. Definitions of terms used. 3. Laws of the pendulum. 4. Uses of the pendulum. Exercises 1. What is the usual shape of the bob of a clock pendulum? Why is this shape used instead of a sphere? 2. Removing the bob from a clock pendulum has what effect on its motion? Also on the motion of the hands? 3. How does the expansion of the rod of a pendulum in summer and its contraction in winter affect the keeping of time by a clock? How can this be corrected? 4. Master clocks that control the time of a railway system have a cup of mercury for a bob. This automatically keeps the same rate of vibration through any changes of temperature. How? 5. How will the length of a seconds pendulum at Denver, 1 mile above sea-level, compare with one at New York? Why? [Illustration: FIG. 82--Escapement and pendulum of a clock.] 6. What is the period of a pendulum 9 in. long? _Note._ In problems involving the use of the third law, use the length of a seconds pendulum for _l_, and call its period 1. 7. A swing is 20 ft. high, find the time required for one swing across the arc. 8. A pendulum is 60 cm. long. What is its period? 9. If in a gymnasium a pupil takes 3 sec. to swing once across while hanging from a ring, how long a pendulum is formed? 10. A clock pendulum makes four vibrations a second, what is its length? Review Outline: Force and Motion Force; definition, elements, how measured, units, dyne. Graphic Representation; typical examples of finding a component, a resultant, or an equilibrant. Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal force, momentum, (_M = mv_), reaction, stress and strain. Moment of Force; parallel forces, couple, effective and non-effective component.