pulley, thus giving four and five strings respectively between the pulleys. Tabulate the results in columns under the headings: Weight f' f" f Work W Work W Number of cords In all cases of ratios like W/f in this experiment and future experiments, work out the values by actual division so that the necessary comparisons can be readily made. For example, in this case compare W/f with the number of cords. EXPERIMENT NO. 114 COEFFICIENTS OF FRICTION. References: Stewart, Physics, Sect. 105-107; Kimball, College Physics, Sect. 74-77; Duff, College Physics, Sect. 11, 30; Spinney, Text-Book of Physics, Sect. 71, 72. It is the purpose of the experiment to show how the coefficients of starting and sliding friction may be found for certain materials, and to prove that starting friction is greater than sliding friction. Tests are also made to show the dependence of friction on nature of the materials in contact but not on the area of the rubbing surfaces. The bed may be a smooth metal plate or a board carefully planed and sandpapered. A pulley is fastened at one end of the bed. Blocks faced with different materials are also needed. See that the surfaces are all wiped clean and dry. Place a block on the bed and run a cord from the block over the pulley to a scale-pan. Be sure that the cord runs parallel to the bed. (a). Set a weight of one kilogram on the block and carefully place weights in the scale-pan until the block just starts to move. No jar must be given to the block. Make several trials. Repeat with loads of 2, 3, etc., up to 6 kilograms. Repeat with the same block resting on a face of smaller area. Repeat with a block faced with another material, in each case recording the names of the materials in contact. If W is the weight of block and load combined, and F is the weight of scale-pan and contents which just starts the block moving, then F/W is the coefficient of starting friction. Compute the coefficients from these trials. (b). Sliding friction. Repeat all the tests of (a) except that weights are now added to the scale-pan until a slight shove on the block is sufficient to produce a slow, uniform motion. Compute the coefficients of sliding friction for the same materials used in (a). (c). Remove the cord and place a single heavy weight on the block. It may be necessary to tie it in place. Tilt the bed slowly till the block just begins to slide, then measure the height and base of the triangle formed between the bed and the table. Make several trials with each combination of materials used in (a) and (b) but with only the one weight in each case. The coefficient of starting friction in this case is the ratio of the height to the base of the triangle, i. e. the tangent of the angle of tilt of the bed. Compare with results of (a). Do your tests show that starting or sliding friction is the greater? What is the effect of area change? Compare coefficients obtained with those given in tables of physical constants. Tabulate under following heads: Weight of Weight of Weight on Weight on FW F/W Block EXPERIMENT NO. 115 THE SIMPLE PENDULUM. References: Stewart, Physics, Sect. 55, 119; Kimball, College Physics, Sect. 101, 128; Duff, College Physics, Sect. 67, 101; Spinney, Text-Book of Physics, Sect. 49. The purpose of this experiment is to study the relation existing between the length and period of a simple pendulum and to compute the acceleration due to gravity. Suspend a small metal sphere from a rigid support by means of a fine wire or a thread. For the first trial make the pendulum 40 cm long. The length of this simple pendulum is the distance between the support and the center of the ball. Adjust the length carefully. The period of the pendulum is the time required for the pendulum to swing from one end of the path to the other end and back again, or the time elapsing between two successive passages through the central point in the SAME direction. To determine the period, we may measure the time required for a fairly large number of complete vibrations. A stop-watch may be used. Press the stem of the watch as the pendulum starts a swing. At the end of that vibration count "one," and continue counting in this way till one hundred vibrations have been made. At exactly the end of the one hundredth vibration press the stem of the watch to stop it. The elapsed time is easily read from the watch. If no stop-watch is to be had, an ordinary watch with a second-hand or the laboratory clock may be used as the timepiece. It must not be thought that the use of a stop-watch insures accurate timing. The tendency is to press the button too late at the beginning and too soon at the end of a run. Even with an ordinary watch, a careful observer can read fractions of a second, but his partner must count vibrations and announce the beginning and ending of a run by some audible signal like the tap of a pencil. Make three determinations of the time for one hundred vibrations and from the mean value calculate the period of the pendulum. In the same manner find the period of the pendulum when it has lengths of 80 cm, 100 cm, 120 cm, and 160 cm. From the equation for the period of a simple pendulum, T-2T g calculate the acceleration of gravity in each of the five cases above. Tabulate your results under the headings: Work out the actual values of the quotients in column three and compare the results for the different pendulums. If the product of two variable quantities is a constant, one quantity is inversely proportional to the other, but if the quotient is constant, one is directly proportional to the other. If one pendulum has twice the period of another, how do the lengths of the pendulums compare? EXPERIMENT NO. 116 DETERMINATION OF GRAVITATIONAL ACCELERATION. References: Stewart, Physics, Sect. 55, 119; Kimball, College Physics, Sect. 101, 128; Duff, College Physics, Sect. 67, 101; Spinney, Text-Book of Physics, Sect. 49. The purpose of this experiment is to determine the gravitational acceleration by means of a simple pendulum, using the method of coincidences. In Experiment No. 115, the same determination was made in a rough way; this method permits much greater accuracy. A large heavy pendulum, of which the time of vibration. has been accurately determined, is mounted near a small simple pendulum. The first part of the experiment consists in determining the period of the simple pendulum by comparison with the large, standard pendulum. This large pendulum may be that of the laboratory clock, if its period has been accurately determined. An electric circuit is so arranged that a buzzer is sounded whenever both pendulums are at rest and making contact with suitably placed mercury cups. Suppose both pendulums are vibrating, and suppose that one pendulum vibrates faster than the other. Then, after a time, there will be an instant when both pendulums are passing through their positions of rest at the same time. The buzzer then sounds. The faster pendulum, however, soon gets ahead of the other, and not until it has gained a half vibration will the buzzer again sound. There are certain advantages to be obtained by using a telegraph sounder or a telephone receiver in place of the buzzer. The time between two successive coincidences is observed. We can compute the number of vibrations the standard pendulum has made in this time, and since the unknown pendulum has made a half vibration more (or less) than the standard, its period may be accurately calculated. cm. Start both pendulums vibrating through small arcs—4 or 5 The simple pendulum is made to swing so that it passes through the mercury contact at every vibration. Light sidewise taps with a pencil accomplish this result. When the buzzer first sounds, write down the time-hour, minute, and second. Owing to the fact that the mercury contact is rather broad, several clicks of the buzzer will be noticed. Write down the time when the last click is heard, and take the mean of the times of the first and last clicks as the true time of coincidence. Allow the pendulums to swing uninterrupted till four coincidences have been observed in the above manner. The time between the first and third coincidences, averaged with the time between the second and fourth coincidences, is the time necessary for one pendulum to gain a complete vibration on the other. Call this time, in seconds, t. Then t divided by the period of the standard should give the number of vibrations made by the standard in this time. (If, owing to experimental error, a whole number is not obtained, take the nearest whole number to the value obtained.) The simple pendulum has made one more (or less) vibration than this. To determine whether or not it has made fewer vibrations than the standard, start both pendulums swinging together, and observe directly which one gains on the other. The period of the simple pendulum may be calculated by dividing the time required for the standard pendulum to make the computed number of vibrations by the number of vibrations made by the simple pendulum during the same time, P = nT n+1 where n is the number of vibrations of the standard pendulum and T its period. With a meter rod measure the distance from the support of the simple pendulum to the top of the ball. Measure the diameter of the ball with a pair of calipers and determine its radius, R. Call the distance from the knife-edge support to the center of the ball, d. Then the length of the equivalent simple pendulum (neglecting the mass of the wire) is, Calculate g from the equation of the simple pendulum: L P2π g |