US3656241A

US3656241A - Experimental derrick and ladder assembly

Info

Publication number: US3656241A
Application number: US30449A
Authority: US
Inventors: Robert F Chambers
Original assignee: Individual
Current assignee: Individual
Priority date: 1970-04-21
Filing date: 1970-04-21
Publication date: 1972-04-18
Anticipated expiration: 1989-04-18

Abstract

Elongate straight beam for demonstrating equilibrium phenomena in classroom physics instruction includes bearing members rotatably mounted at beam ends by pins transversely disposed relative to longitudinal centerline of beam. Lugs rotatably secured to pins at longitudinal centerline of beam have openings for attaching coplanar forces to beam. Elongate straight beam is used as experimental derrick and experimental ladder. Primary objective of derrick experiment is to determine magnitude and direction of reaction force lower support exerts against beam under equilibrium conditions. Magnitude and direction of reaction force found experimentally are compared with theoretically determined values. Primary objective in ladder experiment is to determine magnitude and direction of force lower support exerts against beam under equilibrium conditions. Also, magnitude of force upper support exerts against beam is determined. Experimental values are then compared with theoretical values.

Description

United States Patent Chambers [15] 3,656,241 51 Apr. 18, 1972 [54] EXPERIMENTAL DERRICK AND LADDER ASSEMBLY [72] Inventor: Robert F. Chambers, 504 Beverly Road,

Newark, Del. 19711 [22] Filed: Apr. 21, 1970 21 Appl. No.: 30,449

Related U.S. Application Data [63] Continuation-in-part of Ser. No. 735,259, June 7,

1968, Pat. No. 3,520,981.

[52] U.S. Cl. ..35/19 R [51] Int. Cl. ..G09b 23/08 [58] Field of Search ..35/19 R, 19 A; 46/27, 29; I 49/13 [56] References Cited UNITED STATES PATENTS 3,348,844 10/1967 Lemelson ..273/121 A OTHER PUBLICATIONS 1 L. E. Knott Apparatus Co. Catalog, pp. 123, 124, 125, received Jan. 1917.

Welch'Scientific Co. Catalog, pp. 74, 75, 242, received Oct. 1965.

Primary Examiner-Harland S. Skoqquist Attorney-Connolly & Hutz [57] ABSTRACT Elongate straight beam for demonstrating equilibrium phenomena in classroom physics instruction includes bearing members rotatably mounted at beam ends by pins transversely disposed relative to longitudinal centerline of beam. Lugs rotatably secured to pins at longitudinal centerline of beam have openings for attaching coplanar forces to beam.

Elongate straight beam is used as experimental derrick and experimental ladder. Primary objective of derrick experiment is to determine magnitude and direction of reaction force lower support exerts against beam under equilibrium conditions. Magnitude and direction of reaction force found experimentally are compared with theoretically determined values. Primary objective in ladder experiment is to determine magnitude and direction of force lower support exerts against beam under equilibrium conditions. Also, magnitude of force upper support exerts against beam is determined. Experimental values are then compared with theoretical values.

8 Claims, 8 Drawing Figures PATENTEDAPR 18 I972 SHEET 2 [1F 2 1 EXPERIMENTAL DERRICK AND LADDER ASSEMBLY CROSS REFERENCE TO RELATED APPLICATION The present application is a continuation-in-part application of applicants pending application Ser. No. 735,259, filed June 7, i968 and now U.S. Pat. No. 3,520,981.

BACKGROUND OF THE INVENTION The present invention relates to apparatus for classroom physics experiments, and more particularly to apparatus for demonstrating equilibrium phenomena associated with derricks and ladders.

Many structural arrangements have been proposed for the purpose of demonstrating phenomena associated with the classroom instruction of physics. For the most part, many of these arrangements are characterized by their complex mode of operation as well as the expense of their overall construction. Financially, most of the heretofore available arrangements are beyond the reach of many school systems. The complex nature of most of these arrangements results in lack of interest on the part of the students. Often, physics students lose interest during the particular demonstrations because of the lengthy procedures necessary to achieve a desired result or prove a particular law. Reliable, inexpensive, graphic and simple to use equipment for physics experiments has long been sought by the members of the teaching profession.

Accordingly, it is an object of the present invention to avoid the above disadvantages by providing equipment for classroom physics experiments which is simple to operate and maintain, inexpensive to construct, and reliable throughout continuous use.

Another object of the present invention is to provide an elongate straight beam useful for conducting equilibrium experiments, such as derrick and ladder experiments.

SUMMARY OF THE INVENTION In accordance with the present invention an elongate straight beam is provided for demonstrating equilibrium phenomena in classroom physics instruction. Each end of the beam has a bearing member rotatably mounted to the beam by a pin transversely disposed relative to the longitudinal centerline of the beam. Lugs at the beam ends are rotatably secured to the pins at the longitudinal centerline of the beam, and each lug has an opening at its free end for attaching coplanar forces to the beam ends.

The bearing member at each end of the elongate beam may have a substantially rectangular cross section with the mounting pin at each beam end extending along the longitudinal centerline of the bearing member. Alternatively, each bearing member may have a circular cross section arranged so that its transversely disposed mounting pin extends along the longitudinal centerline of the bearing member. At least several additional lugs are rotatably secured to the beam between the beam ends. The additional lugs are located along the longitudinal centerline of the beam, and the free end portion of each lug has an opening for attaching coplanar forces to the beam.

The elongate straight beam of the present invention may be used in combination with additional structure for constructing an experimental ladder. The additional structure includes upper and lower supports adjacent the beam ends for supporting the beam in an inclined position. A load is attached to the beam between the beam ends at the longitudinal centerline of the beam. The horizontal and vertical components of the force the lower support exerts against the beam are determined by applying horizontal and vertical forces to the lower beam end until the bearing at the lower beam end is slightly shifted away from the lower support. A force applying device is also provided for determining the force a vertical upper support would exert against the beam as a result of the beam pressing against the vertical upper support.

The lower support may comprise an L-shaped bracket that engages the rotatable bearing member secured at the lower beam end; the upper support may be a vertically disposed rectangular sheet that engages the rotatable bearing member secured at the upper beam end. The bearing members may be circular in cross section with the transversely disposed pin at each end of the beam extending along the longitudinal centerline of the bearing member. Altemately, the lower support may comprise a pair of spaced apart rollers that engage the rotatable bearing member at the lower beam end; the upper support may be a roller that engages the rotatable bearing member at the upper beam end. Each rotatable bearing member has a rectangular cross section with its transversely disposed mounting pin extending along the longitudinal centerline of the bearing member.

An experimental derrick apparatus according to the present invention comprises a weighted beam with a hinge pin as- I sembly at the lower end thereof, and a support for the hinge pin assembly. A load is attached to the upper end of the beam and a counteracting force is provided at the upper beam end for maintaining the beam in equilibrium. The horizontal and vertical components of the reaction force the hinge pin assembly exerts against the beam are determined by applying horizontal and vertical forces at the hinge pin assembly until the assembly slightly shifts away from the support.

The experimental derrick may be associated with a series electrical circuit that interconnects the hinge pin assembly and the support. The circuit includes a device for indicating a break therein when the hinge pin assembly is out of contact with the support. The support may comprise an L-shaped bracket, and the hinge pin assembly may include a cylindrical bearing member rotatably connected to the beam by a pin transversely disposed relative to the longitudinal centerline of the beam. The pin extends along the longitudinal centerline of the cylindrical bearing.

BRIEF DESCRIPTION OF THE DRAWING Novel features and advantages of the present invention in addition to those mentioned above will become apparent to those skilled in the art from a reading of the following detailed description in conjunction with the accompanying drawing wherein:

FIG. 1 is a front elevational view of an experimental derrick apparatus according to the present invention;

FIG. 2 is a sectional view taken along line 2-2 of FIG. 1;

FIG. 3 is a front elevational view of an experimental ladder according to the present invention with an alternative approach to the experiment illustrated in phantom outline;

FIG. 4 is a sectional view taken along line 4-4 of FIG. 3;

FIG. 5 is a diagram of the forces associated with the apparatus of FIG. 3;

FIG. 6 is a view similar to FIG. 4 illustrating an alternate embodiment of the ladder of FIG. 3; and

FIG. 7 and 8 are fragmental side elevational views of the alternate embodiment illustrated in FIG. 6.

DETAILED DESCRIPTION OF THE INVENTION Referring in more particularity to FIGS. 1 and 2 of the drawing, an experimental derrick apparatus 300 comprises a beam 302 with a hinge pin assembly or bearing member 304 at the lower end thereof. An L'shaped. support bracket 306 serves to support the hinge pin assembly or hearing 304. As shown in FIG. 1, the L-shaped support bracket 306 is fixed to a support rod 308 at location 310, and the rod rests upon a support surface such as the table 312. The straight elongate beam 302 has a fixed weight 314 suspended from it at location 316, the center of gravity of the beam, along the longitudinal centerline of the beam. The effect of weight 314 is to increase the weight of elongate beam 302. Weight 314 is attached to the beam 302 by a string 317 which in turn is connected to a lug 319 located at the longitudinal centerline of the beam 302 and rotatably supported by a transversely disposed pin 316. A load 318 is attached to the upper beam end by a similar lug 320 rotatably supported at the longitudinal centerline of the beam.

The experimental derrick 300 is maintained in static equilibrium by a weight 322 attached to the upper end of the beam 302 by a string 323 trained about a pulley 324 ad justably secured to the rod 308. The string 323 is secured to the beam thereby simplifying the problem of measuring the magnitude and direction of the force. The present derrick apparatus avoids these disadvantages by providing a realistic the free end of a lug 321 rotatably secured at the upper end of 5 the beam at the longitudinal centerline of the beam. Support structure 325 may be provided to hold the beam in an inclined position until the various weights are adjusted to place the der rick in static equilibrium. Once this is accomplished the support structure 325 is no longer required.

Among the objects of the experimental derrick apparatus 300 is the primary object of determining the magnitude and direction of the reaction force R the support bracket 306 exerts against the beam 302. It is impossible to measure this reaction force directly since both its direction and magnitude are unknown. However, the horizontal and vertical components of the reaction force are in known directions and once these components are determined experimentally, the magnitude and direction of the reaction force may be calculated. The direction of force R from the vertical is represented by angle A, as shown in FIG. 1. When the derrick is in static equilibrium the components of the reaction force R are determined in the following manner. A horizontal force F, is applied to the beam 302 at the hinge pin assembly 304 by weight 326 connected to the hinge pin assembly by a string 328. The string extends from a lug 330 rotatably supported at the center of the beam 302 and runs from that lug to a pulley 332 adjustably attached to a support rod 334. Force F, is applied to the rotatable bearing 304 by a weight 336 connected to the bearing by a lug 338 rotatably supported at the center of the beam 302. A string 340 is connected to the lug 338 and extends vertically upward to a pulley 342. The free end of the string 340 is attached to the weight 336 and the pulley 332 is adjustably attached to the support rod 308. r

A series electrical circuit 350 is provided for interconnecting the hinge pin assembly or bearing 304 and the L-shaped support bracket 306. The circuit 350 includes a power source 352 and an indicator lamp 354 for indicating when the circuit is complete.

The forces Fx and Fy are gradually increased by adding weights to the

strings

328 and 340. This procedure is continued until the force Fy is slightly less than that required to lift the bearing 304 out of contact with the horizontal leg of the L-shaped support bracket 306. Also, the force Fx is adjusted so that it is just large enough to pull the bearing 304 of the beam free of the vertical leg of the L-shaped support bracket 306. When this condition prevails, the series electrical circuit 350 remains complete and the indicator lamp 354 is energized. Force Fy is then gradually increased until the circuit is broken and the lamp goes out. This operation is followed by a gradual reduction in force Fx until the indicator lamp 354 is energized and an increase in force Fx until the lamp goes out. When this condition occurs, the horizontal and vertical components, Fx and F y, of the reaction force R the L- shaped bracket 306 exerts against the beam 302 are measured. The direction and magnitude of the reaction force R are determined by using the Pythagorean theorem and trigonometry. The theoretical reaction force is then calculated by analyzing the forces associated with the derrick. An adjustable protractor 356 is provided for measuring the angles needed to compute the theoretical reaction force. The theoretical values are then compared with the experimentally determined values and found to correspond.

The present apparatus is a realistic approach to analyzing the forces associated with a derrick. For the most part, the heretofore available derrick devices used for demonstration purposes required that the weight of the beam be eliminated as a force in the overall system. Basically, this is accomplished by making the beam extremely light so that the error caused by the beam weight is maintained at a reasonable level. weightless type beams for derrick experiments have been heretofore desired because the line of action of the reaction force the support exerts against the beam will always be along derrick system.

FIGS. 3-7 illustrate an elongate straight beam 400 for demonstrating equilibrium phenomena in classroom physics instruction. More particularly, the beam 400 is utilized as a ladder for determining the force f a wall or upper support 402 exerts against the ladder as a result of the ladder pressing against the wall or support (Newton's Third Law of Motion). This force will act perpendicular to the wall or support 402 since it is assumed that the support, being smooth, will supply no upward frictional force (vertical component for f) to help support the ladder. The experimental setup of FIGS. 3-7 is also utilized to experimentally determine the magnitude and direction of the force the lower support or earth 404 exerts against the beam 400.

The ends of the elongate straight beam 400 include bearing

members

406, 408 rotatably mounted to the beam by

pins

410, 412 transversely disposed relative to the longitudinal centerline of the beam.

Lugs

414, 416, 418 are rotatably secured to the

pins

410, 412 at the longitudinal centerline of the beam 400. Each lug has an opening at its free end for attaching coplanar forces to the beam ends, as described more fully below.

As shown best in FIGS. 3 and 4, each bearing

member

406, 408 may be circular in cross section, and the

supports

402, 404 may comprise rectangular and L-shaped brackets. The mounting pins 410, 412 extend along the centerline of the bearing members while selected portions of the exterior of the bearing members engage the

supports

402, 404. For reasons discussed below, the lower support 404 may include an opening 420 so that a force may be applied along the longitudinal centerline of the beam 400 in the manner best shown in FIG. 3. A lug 422 is provided for attaching this force to the beam 400. Like

lugs

414, 416 the lug 422 is rotatably secured to the pin 410 at the longitudinal centerline of the beam.

Several

additional lugs

424, 426 are rotatably secured to the beam 400 between the beam ends. Each additional lug is located along the longitudinal centerline of the beam, and each lug has an opening at its free end for attaching coplanar forces to the beam.

The ladder experiment illustrated in FIG. 3 is carried out by placing the beam or ladder 400 in equilibrium. This may be accomplished by one or the other of two methods. At the beginning, the weight of beam 400 may be increased by attaching a weight W, to the lug 424 by a string 428. A weight W is attached to the lug 426 by a string 430 for the purpose of simulating the weight of a climber on the ladder. To directly measure the reaction force f the wall 402 exerts on the upper end of a ladder as shown in FIG. 5, pulley 454 is adjusted until string 452 is horizontal. With string 452 in this position, a horizontal force equal to weight 450 is transmitted to lug 418 and pin 412. Weight 450 is increased until the horizontal force on pin 412 is just sufficient to hold bearing member 408 free of support 402. At that time, weight 450 is equal to the reaction force f of the wall.

The components of the reaction force the support 404 exerts on the beam 400 are next determined by applying vertical and horizontal forces to the lower beam end until that end of the beam is free of the lower support 404. The vertical force is applied by a weight 432 connected to the lug 414 by a string 434. The string is trained around a pulley 436 connected by an adjustable bracket 438 secured to a support rod 440. A plumb line 442 assists in adjusting the bracket 438 so that the string 434 is vertical. The horizontal component of the reaction force the support 404 exerts against the beam 400 is experimentally deterrnined by connecting weights 444 to the lug 416 at the lower beam end. A string 446 extends from the lug 416 around an adjustable pulley 448 to the weight 444. The

weights

432 and 444 are adjusted so that they are just sufficient to move the lower beam end out of contact with the support 404.

The various weights described above are manipulated until the beam 400 is slightly out of contact with the upper and

lower supports

402, 404. With the beam in static equilibrium, the various weights are noted and utilized to experimentally determine the magnitude of force f and the magnitude and direction of the reaction forces F. The magnitude of force f is equal to weight 450 and its direction is perpendicular to the wall. The magnitude of force F is computed from its measured horizontal and vertical components F,, F, using the Pythagorean theorm; trigonometry is utilized to determine its direction. The theoretical values of the reaction forces are then calculated and compared with the experimentally determined values. The following table shows by way of example the results obtained with the present equipment.

THE LADDER Angle 55.0 Force W, (grams force) 428 Force W (grams force) 1000 Forcef(experimental 1303 (grams force) Forcef(experimental) 1308 (grams force) 7: Error inf 0.4 Force F, (grams force) I305 Force F, (grams force) 1425 Force F (experimental 1932 (grams force) Force F (theoretical) 1937 (grams force) Error in F 0.3 Angle 6 (experimental 425 Angle 6 (theoretical) 42.5 Error in Angle 0 0 An alternate method of performing the ladder experiment involves the application of forces to the beam 400 which forces are the components of the force f the upper support 402 exerts against the beam 400. This method requires that horizontal and vertical component forces F,, F, first be applied to the lower beam end as before until that end of the beam is just shifted free of the lower support 404. A weight 458 is then attached to the lug 422 at the lower beam end for the purpose of pulling the lower beam end firmly back against the L-shaped support 404. A string 460 trained over an adjustable pulley 462 extends from the weight 458 to the lug 422. The pulley 462 is secured to a bracket 464 slidably connected to the support rod 440. The location of the pulley is adjusted so that the direction of the string 460 is along an extension of the longitudinal centerline of the beam 400. While the lower beam end is held firmly against support 404, weight 450 is connected to the lug 418 at the upper beam end for the purpose of slightly shifting the upper beam end out of contact with the support 402. The weight 450 is connected by string 452 to the lug 418 and the string is trained about the adjustable pulley 454 connected to cross bar support 456. The position of the pulley 454 on the cross bar 456 is adjusted so that the string 452 is exactly perpendicular to the inclined beam 400. A protractor may be used to achieve this relationship. The final adjustment required to place beam 400 in static equilibrium without the aid of

supports

402, 404 involves a reduction in weight 458 until the lower beam end is just pulled free of support 404. Beam 400 will now be in equilibrium under the action of only forces Fx, Fy, f,, f,,, W and W The magnitude of force f can be computed from its components forces f, and f, using the Pythagorean theorm; its direction relative to the wall is found by computing angle a(Alpha).

FIGS. 6 and 7 illustrate an alternate embodiment of the present invention wherein an elongate straight beam 500 has rectangular shaped bearing members 502 rotatably mounted at the beam ends. In this instance, the lower support 504 comprises a pair of spaced apart rollers 506 that engage upper bearing member 502. The upper support is a single roller 507 that engages bearing member 502 at the upper beam end. The support 504 is arranged so as to provide an open area 508 for the same reasons discussed above in conjunction with the embodiment of the invention illustrated in FIGS. 3 and 4.

The elongate straight beam 400 can also be utilized in constructing a derrick experiment for the purpose of studying the forces associated with the derrick. In this regard, the beam 400 can be utilized with other structure to build a setup like the assembly illustrated in FIGS. 1 and 2. The force the lower support exerts on the beam can then be experimentally determined and compared with the theoretical value.

Equilibrium experiments may also be performed with beam 400 in a horizontal position. This requires that the supporting surface of support 402 be in the same horizontal plane as the supporting surface of the lower leg of the L-shaped support 404. Downward parallel forces are applied to beam 400 by attaching weights to lugs that are rotatably secured to pins which are located along the longitudinal centerline of the beam and have openings for attaching coplanar forces. In a similar fashion upward parallel and non-parallel forces are attached to beam 400. One or more lugs at the beam ends which are rotatably secured to the bearing pins at the longitudinal centerline of the beam and have openings for attaching coplanar forces are also utilized. A typical problem may involve the measurement of two forces. One of these forces has an unknown magnitude and a known direction; the other has an unknown direction as well as an unknown magnitude.

What is claimed is:

1. An elongate straight beam for demonstrating equilibrium phenomena in classroom physics instruction, each end of the beam including a bearing member rotatably mounted to the beam by a pin transversely disposed relative to the longitudinal centerline of the beam, lugs at the beam ends rotatably secured to the pins at the longitudinal centerline of the beam, and an opening at the free end of each lug for attaching coplanar forces to the beam ends.

2. An elongate straight beam as in claim 1 wherein each bearing member has a substantially rectangular cross section and its mounting pin extends along the longitudinal centerline of the bearing member.

3. An elongate straight beam as in claim 1 wherein each bearing member has a circular cross section and its mounting pin extends along the longitudinal centerline of the bearing member.

4. An elongate straight beam as in claim 1 including at least several additional lugs rotatably secured along the longitudinal centerline of the beam between the beam ends, and an opening at the free end of each additional lug for attaching coplanar forces to the beam.

5. An elongate straight beam as in claim 1 in combination with structure for constructing an experimental ladder, the structure including upper and lower supports adjacent the beam ends for supporting the beam in an inclined position, a load attached to the beam between the beam ends and along the longitudinal centerline of the beam, and means for determining the horizontal and vertical components of the force the beam exerts on the lower support including horizontal force applying means connected to a lug at the lower beam end for slightly shifting the hearing at the lower beam end away from the lower support in a horizontal direction, and vertical force applying means connected to another lug at the lower beam end for slightly shifting the bearing at the lower beam end away from the lower support in a vertical direction, and means for determining the force the upper support exerts on the beam as a result of the beam pressing against the upper support.

6. The combination of claim 5 wherein the lower support comprises an L-shaped bracket and the upper support comprises a planar vertical surface, the supports engaging the rotatable bearing members at the beam ends, and each rotatable bearing member having a circular cross section with the mounting pin at each beam end extending along the longitudinal centerline of the bearing member.

7. The combination as in claim 5 wherein the lower support comprises a pair of spaced apart rollers that engage the rotatable bearing members at the lower beam end and the upper support comprises a single roller that engages the rotatable bearing member at the upper beam end, and each rotatable bearing member having a rectangular cross section with the mounting pin at each beam end extending along the longitudinal centerline of the bearing member.

8. An experimental derrick apparatus comprising a weighted beam with a hinge pin assembly at the lower end thereof and means supporting the hinge pin assembly, a load attached to the upper end of the beam, a force connected to the upper end of the beam for maintaining the beam in equilibrium, and means for determining the horizontal and vertical components of the reaction force the hinge pin assembly exerts on the beam including horizontal force applying means connected to slightly shift the hinge pin assembly away from the support means in a horizontal direction and vertical force applying means connected to slightly shift the hinge pin assembly away from the support means in a vertical direction whereby the beam is in equilibrium away from the support means when the horizontal and vertical forces are applied to the hinge pin assembly, the hinge pin assembly at the lower end of the weighted beam comprising a bearing member rotatably mounted to the beam by a pin transversely disposed relative to the longitudinal centerline of the beam, a pair of lugs at the lower end of the weighted beam secured to the pin at the longitudinal centerline of the beam, and an opening at the free end of each lug for attaching the horizontal and vertical force applying means.

Claims

5. An elongate straight beam as in claim 1 in combination with structure for constructing an experimental ladder, the structure including upper and lower supports adjacent the beam ends for supporting the beam in an inclined position, a load attached to the beam between the beam ends and along the longitudinal centerline of the beam, and means for determining the horizontal and vertical components of the force the beam exerts on the lower support including horizontal force applying means connected to a lug at the lower beam end for slightly shifting the bearing at the lower beam end away from the lower support in a horizontal direction, and vertical force applying means connected to another lug at the lower beam end for slightly shifting the bearing at the lower beam end away from the lower support in a vertical direction, and means for determining the force the upper support exerts on the beam as a result of the beam pressing against the upper support.