4.2 A needle on the surface of water Now let's study what happens when we place a needle of length = 3 cm on the surface of water in gravity. The surface deforms as shown in Figure 3 - the needle pushes down on the surface, performing work and increasing the potential energy U of the surface as it is deformed from its equilibrium configuration in gravity (completely flat surface). We make a simple model of the surface deformation by saying that for a distancer 1 mm away from the needle, the surface normal deflects an angle 8 = 32 from the vertical. We will now compute the change in surface area and thus energy U) that this produces on the surface of the fluid. The surface tension of water is 7 = 0.073 N/m a) What is hy, the length of the deformed portion of the surface? Use trigonometry to find your answer and it will be helpful to reference the Figure 3. b) What is total area of the deformed region of the surface? For the needle, include the deformed regions of surface on either side of the needle. This is the area of the deformed surface A c) What is surface area of that same region if the needle is removed and the surface was flat? This is the area of the equilibrium surface Ao. d) What is potential energy of the surface when it supports the needle. Again the surface tension of water is n = 0.073 N/m 4.3 The energy of a pair of floating cubes