09:47 4 X L4 Unit 2 Maths A... Page 5 of 11 Engineering Maths Outcome 1: Identify the relevance of mathematical methods to a variety of conceptualised engineering examples Outcome 2: Investigate applications of statistical techniques to interpret, organise and present data Time scale: 6 weeks Mathematical methods and statistical techniques Scenario: You work for in the company \"ATLAS Lifting Systems Inc." that specialises in motors and generators for industrial lifting systems. Your company has introduced a new product line where the efficiency of lifting equipment improved by utilising generators (dynamos) that produce energy when equipment is being lowered. Your supervisor asks you to produce calculations for the sales team that showcase the potential energy savings of these adaptations. Part 1: Theoretical Model You have been asked to model the energy savings for a given scenario. The theoretical maximum energy (ignoring all heat losses) generated by the dynamo is given by the difference between the potential energy of the load at the start and the kinetic energy at the end (see Eq. 1). You have also researched the following formulas to help you complete the calculations: Max dynamo energy: Edwum = 1m, Ekm (Eq. 1) List of variables: Potential energy: El",c = mgh (Eq. 2) E: energy (I) g: 9.81 (Tn/$2) Kinetic ener : E - =1nm2 E .3 "'1 mass \"'37) '1 time (5' . \"9" \""1 2 ( q ) 17: velocity (m/s) h: height (m) Linear motion: :1 = 20' + v)t (Eq. 4) d: distance (m) An object with a mass m = 25kg and an initial velocity of u = 0 mls is lowered from a height of h within 1 = Tseconds (T provided Table 1). A. Calculate the following (showing dimensional consistency in all formulas): a. The potential energy of the product at the start (h = 1.4 m) b. The nal velocity v of the object o. The kinetic energy of the product at the end (using the nal velocity). d. The maximum (theoretical) amount of energy converted by the dynamo. B. Additionally, use dimensional analysis to derive the formulas for: 1 a. The average power Pavg (Watts), given energy E (Joules) h and time t (seconds). b. The electric power Pelee (Watts), given voltage (Volt) and resistance (Ohm). Page 6 of 11