Hydrometer-Spring balance instrument

Hydrometer-Spring balance instrument CLAUDE ZIAD BAYEH 1, 2 1 Faculty of Engineering II, Lebanese University 2 EGRDI transaction on physics (2001) LEBANON Email: claude_bayeh_cbegrdi@hotmail.com NIKOS E.MASTORAKIS WSEAS (Research and Development Department) http://www.worldses.org/research/index.html Agiou Ioannou Theologou 17-2315773, Zografou, Athens,GREECE mastor@wseas.org Abstract: - The Hydrometer-Spring Balance is a new instrument introduced by the authors in physics in order to simplify the manipulating of two instruments which are the Hydrometer that measure the density of the liquid and the spring balance that measure the mass of an object inside and outside the liquid. So the new instrument can be used instead of the two traditional instruments. The new instrument will be put in a graduated cylinder filled with water and this will facilitate the measurement of the volume of the displaced water that is equal to the volume of the object, so we can measure at the same time the mass of the object and its volume therefore we can deduce the density of the object with respect to the density of water. The new instrument allows us to measure also the density of other liquids such as alcohol, benzene, oil, milk, salt water, petroleum products with respect to the density of the water. Key-words:-Buoyant force, Archimedes principles, Hydrometer, Spring balance, liquid, instrument. 1 Introduction In physics, A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water. A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall container, often a graduated cylinder, and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a scale inside the stem, so that the specific gravity can be read directly. Varieties of scales exist, and are used depending on the context. In this paper, the authors developed a new instrument called Hydrometer-Spring balance because it will simplify the two instruments Hydrometer and Spring balance into only one instrument. This instrument is capable to measure the density of the liquid and at the same time is can measure the mass and weight of an object above and under the liquid. This instrument can be helpful for measuring sinking objects only and not for the floating objects because the buoyant force is equal to the weight. We should use also a graduate test tube (graduate tall container) in order to facilitate the calculation. The Hydrometer-Spring balance can be found in many scales and sizes according to the usage. In this paper the authors develops the basic principle of the new instrument and brief examples are given in order to understand how this instrument works. In the section 2, the Archimedes s principle is presented. In the section 3, Hydrometer-Spring balance principle is presented with simple example. And finally in the final section a conclusion is presented. 2 Archimedes s principle Archimedes' Principle, law of physics that states that when an object is totally or partially immersed in a fluid, it experiences an upthrust (or buoyant force) equal to the weight of the fluid displaced. The principle is most frequently applied to the behavior of objects in water, and helps to explain floating and sinking, and why objects seem lighter in water. It also applies to balloons in the air. FF BB = mmmm = ρρρρρρ (1) With FF BB is the buoyant force or Upthrust ρρ is the density of the liquid or object (g/cm3 or kg/m3) ISBN: 978-1-61804-142-5 81

VV is the Volume of liquid displaced or the volume of the object that immersed in the liquid (cm3 or m3). gg = 9.81NN/kkkk is the gravity constant. Buoyant force = weight the object floats and stationary Buoyant force > weight the object moves up Buoyant force < weight the object moves down Fig. 2: represents the Hydrometer instrument. This instrument measures the density of a liquid. Fig. 1: represents an object immersed in a liquid and two forces are applied on this object, the weight force and the buoyant force. The warm liquid is less dense than the cold liquid. 3 Hydrometer instrument and Spring balance instrument 3.2 Spring balance instrument The spring balance (spring scale apparatus) is simply a spring fixed at one end with a hook to attach an object at the other. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position. Therefore the scale markings on the spring scale are equally spaced. 3.1 Hydrometer instrument A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water. A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall container, often a graduated cylinder, and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a scale inside the stem, so that the specific gravity can be read directly. Varieties of scales exist, and are used depending on the context. ISBN: 978-1-61804-142-5 82

Fig. 3: represents the Spring balance instrument. This instrument measures the mass of an object inside a liquid. 4 Hydrometer-Spring balance principle This instrument is invented by the authors. The principle of the instrument Hydrometer-Spring balance is very simple. It is composed by a graduate stem that contains two scales, one for the density of the liquid and the other for the mass of the object posed on the plate (Figure 4). It contains also a plate on the top of the graduate stem in order to put an object and measure its mass when the instrument is immersed in the water. The scale of mass is presented in the left part of the stem. It contains also in the bottom a head of lead in order to put it upright when it is immersed in the water. It contains also two hooks of thin aluminum that can be fold in order to maintain the object under the water. The scales in the left part of the stem is to measure the density of the liquid, when the instrument is immersed in the liquid, the surface of the liquid will be at the same level as indicated on the graduate scale specified for the density. So we can read easily the value of the density. (Refer to figure 5) The density of the potable water is equal to 1 g/cm3. And this is a reference for other liquids. Fig. 4: represents the instrument Hydrometer-Spring balance. ISBN: 978-1-61804-142-5 83

Fig. 5: represents the instrument Hydrometer-Spring balance immersed in a liquid. In figure 5, we can measure the density of the liquid. For example it is equal to 1.2g/cm3. The density of the water is equal to 1g/cm3. Fig. 6: represents the instrument Hydrometer-Spring balance immersed in a liquid with an object posed on the plate. 4.1 Calculating the mass of an object To calculate the mass of an object we have to fill the graduate tall container with water and immerse the instrument in the water until indicate the value 1g/cm3 on the scale. Then we put an object on the plate (Figure 6) and measure its mass in (g) as indicated in the left part of the stem. For example it is equal to 20g in the figure 6. (We look at the left part of the stem when the graduate scale is for the mass) mm oooooooooooo = 20gg (2) 4.2 Calculating the volume of an object To calculate the volume of an object we have to fill the graduate tall container with water and immerse the instrument in the water until indicate the value 1g/cm3 on the scale. At the same time we look at the graduate scale of the tall container (figure 8). In the figure 7, the volume indicated is equal to 101ml ISBN: 978-1-61804-142-5 84

We can also calculate the apparent weight of the object in the water with WW aa = mm gg = 10 9.81 = 98.1 NNNNNNNNNNNN Fig. 7: represents the instrument Hydrometer-Spring balance immersed in a liquid. The next step is to put the object under the water folded by the hooks (figure 8), and the instrument will descend until give the exact value of the volume indicated on the graduate tall container. For example VV oooooooooooo = 111 101 = 10mmmm = 10cccc3 (refer to figure 8) Therefore, We have calculated the mass of the object and the volume of the object so it is easy to calculate the density of the object using the following formula: ρρ oooooooooooo = mm oooooooooooo (3) VV oooooooooooo In our example it is equal to: ρρ oooooooooooo = mm oooooooooooo = 20gg = 2gg/cccc3 = VV oooooooooooo 10cccc 3 2000kkkk/mm3 We can also calculate the weight of the object with WW = mm gg = 20 9.81 = 196.2NNNNNNNNNNNN Fig. 8: represents the instrument Hydrometer-Spring balance immersed in a liquid with an object folded by the hooks under the water. 5 Conclusion The Hydrometer-Spring Balance is a new instrument introduced by the authors in physics in order to simplify the manipulating of two instruments which are the Hydrometer that measure the density of the liquid and the spring balance that measure the mass of an object inside and outside the liquid. So the new instrument can be used instead of the two traditional instruments. The new instrument will be put in a graduated cylinder filled with water and this will facilitate the measurement of the volume of the displaced water that is equal to the volume of the object, so we can measure at the same time the mass of the object and its volume therefore we can deduce the density of the object with respect to the density of ISBN: 978-1-61804-142-5 85

water. The new instrument allows us to measure also the density of other liquids such as alcohol, benzene, oil, milk, salt water, petroleum products with respect to the density of the water. We can have many sizes and volumes of this instrument according to the utilization. As conclusion, this instrument replaces two other instruments which are used to determine the volume and mass and density of a liquid or an object. References: [1] Mariam Rozhanskaya, I. S. Levinova, "Statics", in Rashed, Roshdi; Morelon, Régis, Encyclopedia of the History of Arabic Science, 1 & 3, Routledge, ISBN 0-415-12410-7, pp. 614 642, (1996). [2] Charles Thomas Davis, The manufacture of leather: being a description of all of the processes for the tanning and tawing with bark, extracts, chrome and all modern tannages in general use, H. C. Baird & co., 1897. [3] "Acidometer", The Free Dictionary. Farlex. 2003. [4] Acott, Chris (1999). "The diving "Law-ers": A brief resume of their lives.". South Pacific Underwater Medicine Society journal 29 (1). ISSN 0813-1988. OCLC 16986801. (1999) [5] The first Eureka moment, Science 305: 1219, (August 2004). [6] CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59 ISBN: 978-1-61804-142-5 86