A wagon weighing 5100 Kg moving at a speed of 8 km/h has to be brought...

 

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A wagon weighing 5100 Kg moving at a speed of 8 km/h has to be brought to rest. Springs made of wire diameter 25mm with a Dm of 250mm and with 24 turns are available. Find the number of springs required in buffer to stop the wagon at a compression of 180mm. [G= 84GPa]. [Hint: You need to use formula for kinetic energy and work done in your solution] (10 marks) b) & c) A close coiled helical spring is made of diameter wire 25mm. The spring index (C) is 8. Find the number of turns required and maximum allowable load if the allowable shear stress is 100 MPa and elongation is limited to 40mm. [G-80 GPa]. Use the Wahl factor in your calculations. A wagon weighing 5100 Kg moving at a speed of 8 km/h has to be brought to rest. Springs made of wire diameter 25mm with a Dm of 250mm and with 24 turns are available. Find the number of springs required in buffer to stop the wagon at a compression of 180mm. [G= 84GPa]. [Hint: You need to use formula for kinetic energy and work done in your solution] (10 marks) b) & c) A close coiled helical spring is made of diameter wire 25mm. The spring index (C) is 8. Find the number of turns required and maximum allowable load if the allowable shear stress is 100 MPa and elongation is limited to 40mm. [G-80 GPa]. Use the Wahl factor in your calculations.

Answer rating: 100% (QA)

To solve these questions we need to apply the formulas for kinetic energy work done and the equations related to helical springs Lets solve them step by step a Stopping the Wagon with Buffer Springs Given Mass of the wagon m 5100 kg Initial velocity v 8 kmh 8 10003600 ms 83 ms Compression distance x 180 mm 1801000 m First lets calculate the initial kinetic energy KE of the wagon using the formula KE 12 m v2 KE 12 5100 832 KE 12 5100 649 KE 1824009 J To bring the wagon to rest the work done W by the buffer springs will be equal to the initial kinetic energy The formula for work done by a spring is given by W 12 kx2 where k is the spring constant We need to calculate the spring constant k using the formula k Gd464D3n Given Wire diameter d 25 mm 251000 m Mean diameter Dm 250 mm 2501000 m Number of turns n 24 Shear modulus G 84 GPa 84109 Pa Lets substitute the values into the formula to find the spring constant k k 84109 2510004 64 2501000324 k 21000000 Nm Now substitute the values of W k and x into the work done equation ... View the full answer