EXPERIMENT NO. 117

SURFACE TENSION.

References: Stewart, Physics, Sect. 161-164; Kimball, College Physics, Sect. 254-257, 262; Duff, College Physics, Sect. 123-125; Spinney, Text-Book of Physics, Sect. 146-148, 150.

The purpose of this experiment is to determine the surface tension of water and soap-solution from measurements of the rise of the liquids in capillary tubes. The exposed surface of any liquid shows a tendency to contract, which accounts for the formation of spherical drops, and the elevation or depression of the liquids in small tubes, as well as many other phenomena. The contractile force per UNIT LENGTH of film for a given liquid is called the surface tension. The presence of salt, grease, or almost any impurity will alter the surface tension, so extreme caution as to cleanliness must be exercised or results will be in error. Surface tension measurements are of great importance in modern medical research and also in studies of plant nourishment and the phenomena of soils.

It is shown in text-books of physics that the elevation or depression of a liquid in a capillary tube is related to the surface tension and density of the liquid and the radius of the tube by the formula:

Τ T=ir hd g.

We can measure r and h; g is the gravitational acceleration, so T can be computed.

The tubes furnished will be clean. Other parts of the apparatus should be rinsed in tap water and then in distilled water, and perhaps treated with cleaning solutions if there are traces of grease on them. Mount three tubes of different diameters side by side on the centimeter scale by means of a rubber band or bit of soft wax placed near the top of the tubes. Set the scale vertically in a wooden clamp so that the lower ends of the scale and tubes are several millimeters below the surface of some distilled water in a crystallizing dish. Look along the UNDER side of the surface of the water in the dish and read the scale. Read also the tops of the water columns and then determine h, the actual heights to which the water has climbed in the three tubes.

Place a bit of soft wax on the glass microsco the three sections of tube in the wax with the n uppermost. Mount the slide on the stage microscope, focus the instrument on the top of the exact number of turns and fractions of a t necessary to move the cross-wire across the ima the tube. Do this for each tube. Then find the of the micrometer screw which correspond to This number may be given by the instructor or by focusing the instrument on a suitable scale turns necessary to shift the cross-wire one scale pute the radii of the tubes. Remember that the inverted and perverted images, so that the tube its image on the left.

Obtain the value of d for the water at the ature and then compute the surface tension, T. it measured? Compare with values given in ta Repeat using soap-solution. Is the surfac or less than that of water? Does this agree wit on the matter?

EXPERIMENT NO. 118

HOOKE'S LAW-YOUNG'S MODULU

References: Stewart, Physics, Sect. 172-177; Physics, Sect. 234-238, 243; Duff, Colle 51-56; Spinney, Text-Book of Physics, Se

You

There are several coefficients of elasticity, e as the ratio between a stress and a strain. the ratio between tensile stress and tensile strai found by measuring the elongations of a giver known weights.

A brass wire, approximately two meters lo a rigid support near the ceiling. The lower en angular brass frame sliding in a slot cut throu

A weight-pan is hung on the under side of this frame. As the load in the pan is increased, the wire is stretched, but the elongation is so small that special methods must be used to meaure it accurately. A number of methods have been devised; only one of which will be described here, that involving the optical lever. This lever is a three-legged device carrying an adjustable mirror. The rear leg is set in the rectangular brass frame while the two front legs rest on the shelf through which the frame passes. If the wire is stretched, the mirror is tilted a little. A reading telescope, with a vertical scale beside it, is set up some distance in front of the mirror, and is focused on the image of the scale seen in the mirror. If the cross-wire of the telescope is set horizontally, it is easy to take a reading of the scale and to detect any change in the reading.

Place 500 grams in the pan to take up all slack in the system and read the position of the cross-wire to the nearest tenthmillimeter. This reading is the starting point and the "zeroload" is not to be counted as part of the stretching force. Then carefully add 400 grams to the pan and read again. Continue adding 400-gram weights and taking the readings until 2000 grams have been added. Then remove 400 grams at a time, reading the scale as before. In order to compute the average stretch caused by 400 grams, subtract the initial reading from each of the others in turn and divide each difference by the corresponding number of 400-gram weights on the pan at the time. Measure L, the length of the wire. With a micrometer, find the diameter of the wire and compute A, the cross-sectional area in square centimeters.

The difference in readings on the scale is not the true elongation of the wire, but we can calculate the elongation from this difference in the following manner:

Let S be the mean change in scale-reading caused by the addition of 400 grams, R the distance from mirror to scale, r the perpendicular distance from the rear point of the lever to the line joining the other two points. We can find r best by making an impression of the points on a piece of paper.

Now, if the wire stretches an amount e, the mirror is turned through an angle e/r, and the reflected light is of course turned through twice this angle. But the angle turned through by the reflected light is equal to S/R. Therefore,

2R

Tabulate data as follows:

Load in Scale reading Elongation Stress

dynes

F

e

F

A

Make one computation of the average stress weight, first reducing the grams-weight to dynes age elongation caused by a 400-gram load and strain. The ratio between the stress and st Modulus. State Hooke's Law and show how dicate its truth. Which will cause the greater Modulus, a mistake of 0.01 cm in the diameter of 1 cm in the length measurement?

EXPERIMENT NO. 119

ELASTICITY OF A BENDING BEA

References: Stewart, Physics, Sect. 176, 181; Physics, Sect. 243, 244; Duff, College Ph Spinney, Text-Book of Physics, Sect. 92

To test Hooke's Law and compute You measurements made on a bending beam is th experiment.

Place a square steel rod, about 7 mm squ long, across the tops of two upright supports an pan to hang from the center of the beam. Pl the pan as an initial load to take up all pos apparatus before beginning the measurements loads upon the pan, 200 grams at a time, rea of the beam for each load, till six or seven su been made, and then remove them step by step

"zero-load" is left. The amount of bending may be measured by a meter stick clamped upright behind the beam, by a mirror scale, by a lever device, or by a micrometer screw. It is left to the student to find out how to compute the actual deflection of the beam from the indications of the measuring device. If the beam is too stiff for an appreciable bend to be caused by 200 grams, larger weights must be used. With wooden rods, smaller forces may be employed if the bar sags too much. Test two or three different rods.

Tabulate the data under the headings, "Load," "Scale reading,' ""Deflection." Plot a curve with loads as abscissae and deflections as ordinates. Does the form of the curve agree with that demanded by Hooke's Law? Find the average bend caused by the 200-gram load and calculate Young's Modulus, E, for the materials tested, by using the formula,

where W = weight in dynes, L = length between supports, D= bend, B breadth of the beam in cm. and T― thickness in a vertical plane in cm.

EXPERIMENT NO. 120

CENTRIFUGAL FORCE.

References: Stewart, Physics, Sect. 74-77; Kimball, College Physics, Sect. 113-118; Duff, College Physics, Sect. 82, 87, 88; Spinney, Text-Book of Physics, Sect. 41-43.

In order to keep a mass traveling at uniform speed in a circular path, a constant force must act toward the center of the circle along a radius. This force is known as the centripetal force, and the equal reaction-which must exist according to the Third Law of Motion-is called the centrifugal force. It is proved in text-books of physics that the magnitude of either of these forces is given by the formula,