Drawing pins Michal Hledík 7.

7. Drawing pins A drawing pin (thumbtack) floating on the surface of water near another floating object is subject to an attractive force. Investigate and explain the phenomenon. Is it possible to achieve a repulsive force by a similar mechanism? 2

Video of attracting +picture of pins 3

Content 1.Deformation of water surface 2.Attraction of pins Mechanism Calculating the motion Theory vs. experiments 3.Repulsion of objects Mechanism Attracting/repelling boundary 4

1. Deformation of water surface 5

Forces analysis Gravity Buoyant force Surface tension Force equilibrium 6

Only unknown quantities Eq. (1) 7

Water displacement Absent water – compensated by surface tension Pressure – hydrostatic 8

Water displacement Resulting function: Dominic Vella, L. Mahadevan, The ‘‘Cheerios effect,’’ (2005) ` ` ` ` 9

Finding contact angle Eq. (1): Predicted angle: 10

Contact angle measurement Analyzing size of shade of the pin Distant light source Pin on water 11

Measuring the contact angle Applying Snell’s law, fitting contact angle (size of the shade) Contact angle: 12

Shape of water surface [mm] 13

2. Attraction of pins 14

Why are they attracting? 2 pins on water – inclined to each other Potential energy of water and pin – decreases as pin descends Mass of a pin > mass of water displaced 15

Determining the acceleration Horizontal motion: β 16

Slope of one pin Given by the deformation of water surface by the other pin Our approximation: 17

Drag force Assuming …position Video analysis and fit 18

Fitting the drag coefficient Distance passed x [m] Time [s] 19

Acceleration  distance in time Dependence of acceleration on distance and velocity Numerical solution 20

Attracting – experiment 21

Theory vs. experiment Distance of the pins [mm] Time [s] 22

3. Repelling objects 23

Repulsive force Object wetted by water  acts downwards  object floats up 24

Repelling objects Plastic caps from pins – float upwards There is a critical mass – does not repel or attract Behavior depends on weight 25

Both caps wetted by water 26

+ A little weight on the yellow cap 27

Empty cap and a cap with a weight Time [s] Distance between the caps [cm] 0,027g 0,041g 0,062g 0,162g 0,204g Greater mass  stronger repulsion 28

Conclusion We explained the mechanism of ‒ floating, attraction, repulsion Determined the deformation of water surface Described the motion quantitatively ‒ theory correlates with experiments Found the border between attraction/repulsion Thank you for your attention 29

APPENDICES 7. Drawing pins

Drawing pin “dipole” – attracts different objects on different sides 31

` Water displacement Boundary conditions: Solution: Dominic Vella, L. Mahadevan, The ‘‘Cheerios effect,’’ (2005) 32

Critical mass Water is not deformed Surface tension resultant force = 0 33

Critical mass Pin caps – bent edges Mass theoretically: Depth: Mass experimentally: 34