The Floating Needle

Abstract

A mathematico-physical treatment of the floating (on water) needle system is presented. Gravitational potential energy, buoyancy, surface energy, and interfacial energy are taken into account. The floating is regarded as a metastable state resulting from a minimum in the curve relating the energy to the distance of descent. It is shown that such an energy minimum arises naturally out of the mathematics needed to evaluate the factors mentioned above. The calculations are supplemented with simple experiments with paper clips and an aluminum nail ("pseudo-needles"), which lead to approximate upper limits to the diameters of cylindrical metal rods of different densities that can be floated on water.

The Molecular Boat: A Hands-On Experiment To Demonstrate the Forces Applied to Self-Assembled Monolayers at Interfaces

“…Changes in the contact angle between water and the water–substrate interface alters the maximum load the substrate can carry before sinking. A quantitative description of the relationship between contact angle, surface geometry, and floatation has been previously detailed, and in summary, this analysis shows that maximum load is related to the perimeter of the object and the three-phase contact angle. ,, …”

“…A quantitative description of the relationship between contact angle, surface geometry, and floatation has been previously detailed, and in summary, this analysis shows that maximum load is related to the perimeter of the object and the threephase contact angle. 14,21,22 To test the effect of SAM functionalization on floatation, three sets of ODTS, APTMS, and based-etched glass substrates were placed on the surface of water and external masses (staples) were added every 5 s until the substrates sank (Figure 2). The maximum force sustained by each substrate was calculated by summing the mass of the coverslip with the mass of the external load and determining the corresponding force of gravity.…”

“…When the substrate is afloat, the factors that need to be considered are the force of gravity, buoyancy, surface tension, and the SAM–water interfacial tension. At equilibrium, it is possible to directly calculate the force of gravity and the surface tension force ( F γ = (perimeter of substrate) × cos­(θ) × 72 mN/m), however, the buoyancy force (see “dimple” formed on the water surface in Figure ) or the interfacial tension cannot be easily determined within the scope of this lab. ,, Nonetheless, molecular functionalization of the substrate provides for a facile method to alter the contact angle of the water–substrate interface, thereby changing the buoyancy force and surface and interfacial tensions while keeping the mass effectively constant. In fact, if the water–SAM interfacial tension was assumed to be zero, then the magnitude of the buoyancy force can be experimentally determined from the literature values of F γ and the measured mass of the substrate.…”

“…13 This phenomenon is also commonly demonstrated with the floating needle experiment where a metal paper clip or needle will float on the surface of water. 14 The ability to visualize floatation makes surface tension a tangible concept for students and a well-suited method of characterizing the effects of surface modification. 15,16 In this laboratory experiment, glass coverslips float on water because the force of gravity is at equilibrium with counteracting buoyancy and surface tension (capillary force) of the water and interfacial tension.…”

Axisymmetric Liquid Hanging Drops

“…Articles in this Journal cover the capillary-rise method (6)(7)(8)(9), the bubble-pressure method (6,(10)(11)(12)(13), force methods using du Noüy ring or Wilhelmy plate (14)(15)(16)(17)(18), goniometry on the sessile drop (19)(20)(21)(22)(23), the vibrating-jet method (24), and the drop-mass or volume method (25)(26)(27). A novel and interesting treatise of the floating-needle experiment has been recently published by Condon et al (28) who calculated energy versus immersion depth curves for cylindrical metal needles in water.…”