International Journal of Pure and Applied Mathematics Volume 119 No. 12 2018, 3083-3089 ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu VELOCITY Dr.R.Krithiga1, Dr. N.Selvi2 Associate Professor 1 2 Department of Physics, BIST, BIHER, Bharath University, Chennai. [email protected] Terminal velocity and free fall are two related concepts that tend to get confusing because they depend on whether or not a body is in empty space or in a fluid (e.g., and atmosphere or even water). Take a look at the definitions and equations of the terms, how they are related, and how fast a body falls in free fall or at terminal velocity under different conditions. Terminal Velocity Definition Terminal velocity is defined as the highest velocity that can be achieved by an object that is falling through a fluid, such as air or water. When terminal velocity is reached, the downward force of gravity is equal to the sum of the object's buoyancy and the drag force. An object a terminal velocity has zero net acceleration. Terminal Velocity Equation There are two particularly useful equations for finding terminal velocity. The first is for terminal velocity without taking into account buoyancy: 1/2 Vt = (2mg/ρACd) where: Vt is the terminal velocity m is the mass of the object that is falling g is acceleration due to gravity Cd is the drag coefficient ρ is the density of the fluid through which the object is falling A is the cross-sectional area projected by the object In liquids, in particular, it's important to account for the buoyancy of the object. Archimedes' principle is used to account for the displacement of volume (V) by the mass. The equation then becomes: 1/2 Vt = [2(m - ρV)g/ρACd] Free Fall Definition 3083 International Journal of Pure and Applied Mathematics Special Issue The everyday use of the term "free fall" is not the same as the scientific definition. In common usage, a sky diver is considered to be in free fall upon achieving terminal velocity without a parachute[1-5]. In actuality, the weight of the sky diver is supported by a cushion of air. Free fall is defined either according to Newtonian (classical) physics or in terms of general relativity. In classical mechanics[6-11], free fall describes the motion of a body when the only force acting upon it is gravity. The direction of the movement (up, down, etc.) is unimportant. If the gravitational field is uniform, it acts equally on all parts of the body, making it "weightless" or experiencing "0 g". Although it might seem strange, an object can be in free fall even when moving upward or at the top of its motion[12-18]. A skydiver jumping from outside the atmosphere (like a HALO jump) very nearly achieves true terminal velocity and free fall. In general, as long as air resistance is negligible with respect to an object's weight, it can achieve free fall. Examples include: A spacecraft in space without a propulsion system engaged An object thrown upward An object dropped from a drop tower or into a drop tube A person jumping up In contrast, objects not in free fall include A flying bird A flying aircraft (because the wings provide lift) Using a parachute (because it counters gravity with drag and in some cases may provide lift) A skydiver not using a parachute (because the drag force equals his weight at terminal velocity) In general relativity, free fall is defined as the movement of a body along a geodesic, with gravity described as space-time curvature. Free Fall Equation If an object is falling toward the surface of a planet and the force of gravity is much greater than the force of air resistance or else its velocity is much less than terminal velocity[19-25], the vertical velocity of free fall may be approximated as: vt = gt + v0 where: 3084 International Journal of Pure and Applied Mathematics Special Issue vt is the vertical velocity in meters per second v0 is the initial velocity (m/s) g is the acceleration due to gravity (about 9.81 m/s2 near Earth) t is the elapsed time (s) How Fast Is Terminal Velocity? How Far Do You Fall? Because terminal velocity depends on drag and an object's cross section, there is no one speed for terminal velocity. In general, a person falling through the air on Earth reaches terminal velocity after about 12 seconds[26-30], which covers about 450 meters or 1500 feet. A skydiver in the belly-to-earth position reaches a terminal velocity of about 195 km/hr (54 m/s or 121 mph). If the skydiver pulls in his arms and legs, his cross section is decreased, increasing terminal velocity to about 320 km/hr (90 m/s or just under 200 mph)[31-35]. This is about the same as the terminal velocity achieved by a peregrine falcon diving for prey or for a bullet falling down after having been dropped or fired upward[36-45]. The world record terminal velocity was set by Felix Baumgartner, who jumped from 39,000 meters and reached a terminal velocity of 134 km/hr (834 mph). References 1. Ramamoorthy, R., Kanagasabai, V., Kausalya, R., Impact of celebrities' image on brand, International Journal of Pure and Applied Mathematics, V-116, I-18 Special Issue, PP-251-253, 2017 2. Ramamoorthy, R., Kanagasabai, V., Vignesh, M., Quality assurance in operation theatre withreference to fortis malar hospital, International Journal of Pure and Applied Mathematics, V-116, I-14 Special Issue, PP-87-93, 2017 3. Ramya, N., Arthy, J., Honey comb graphs and its energy, International Journal of Pure and Applied Mathematics, V-116, I-18 Special Issue, PP-83-86, 2017 4. Ramya, N., Jagadeeswari, P., Proper coloring of regular graphs, International Journal of Pure and Applied Mathematics, V-116, I-16 Special Issue, PP-531-533, 2017 5. Ramya, N., Karunagaran, K., Proper, star and acyclic coloring of some graphs, International Journal of Pure and Applied Mathematics, V-116, I-16 Special Issue, PP- 43-44, 2017 6. Ramya, N., Muthukumar, M., On coloring of 4-regular graphs, International Journal of Pure and Applied Mathematics, V-116, I-16 Special Issue, PP-491-494, 2017 7. Ramya, N., Muthukumar, M., On star and acyclic coloring of graphs, International Journal of Pure and Applied Mathematics, V-116, I-16 Special Issue, PP-467-469, 2017 8. Ramya, N., Pavi, J., Coloring of book and gear graphs, International Journal of Pure and Applied Mathematics, V-116, I-17 Special Issue, PP-401-402, 2017 3085 International Journal of Pure and Applied Mathematics Special Issue 9. Ramya, P., Hameed Hussain, J., Alteration framework for integrating quality of service in internet real-time network, International Journal of Pure and Applied Mathematics, V-116, I-8 Special Issue, PP-57-61, 2017 10. Ramya, P., Sriram, M., Tweet sarcasm: Peep, International Journal of Pure and Applied Mathematics, V-116, I-10 Special Issue, PP-231-235, 2017 11. Sabarish, R., Meenakshi, C.M., Comparision of beryllium and CI connecting rod using ansys, International Journal of Pure and Applied Mathematics, V-116, I-17 Special Issue, PP-127-132, 2017 12. Sabarish, R., Rakesh, N.L., Outcome of inserts for enhancing the heat exchangers, International Journal of Pure and Applied Mathematics, V-116, I-17 Special Issue, PP- 419-422, 2017 13. Sangeetha, M., Gokul, N., Aruls, S., Estimator for control logic in high level synthesis, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP- 425-428, 2017 14. Sangeetha, M., Gokul, N., Aruls, S., Image steganography using a curvelet transformation, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-417-422, 2017 15. Saraswathi, P., Srinivasan, V., Peter, M., Research on financial supply chain from view of stability, International Journal of Pure and Applied Mathematics, V-116, I-17 Special Issue, PP-211-213, 2017 16. Saravana Kumar, A., Hameed Hussain, J., Expanding the pass percentage in semester examination, International Journal of Pure and Applied Mathematics, V-116, I-15 Special Issue, PP-45-48, 2017 17. Saravana, S., Arulselvi, S., AdaBoost SVM based brain tumour image segmentation and classification, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-399-403, 2017 18. Saravana, S., Arulselvi, S., Dynamic power management monitoring and controlling system using wireless sensor network, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-405-408, 2017 19. Saravana, S., Arulselvi, S., Clustered morphic algorithm based medical image analysis, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-411-415, 2017 20. Saravana, S., Arulselvi, S., Networks, International Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-393-396, 2017 21. Saritha, B., Chockalingam, M.P., Adsorptive removal of heavy metal chromium from aqueous medium using modified natural adsorbent, International Journal of Civil Engineering and Technology, V-8, I-8, PP-1382-1387, 2017 22. Saritha, B., Chockalingam, M.P., Adsorptive removal of brilliant green dye by modified coconut shell adsorbent, International Journal of Pure and Applied Mathematics, V-116, I-13 Special Issue, PP-211-215, 2017 23. Saritha, B., Chockalingam, M.P., Photodegradation of eriochrome black-T dye from aqueous medium by photocatalysis, International Journal of Pure and Applied Mathematics, V-116, I-13 Special Issue, PP-183-187, 2017 3086 International Journal of Pure and Applied Mathematics Special Issue 24.