A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 10^8 N/m ^2 and its radius is 4 mm, then maximum acceleration the lift can take is _______ m/s ^2 . (take g = 10 m/s ^2 and = 3.14 )

Step-by-step solution

Maximum stress _ max = 4 10^8 N/m ^2 Radius of wire r = 4 10⁻³ m Mass of lift m = 1600 kg Maximum tension the wire can withstand is given by: T_ max = _ max r^2 T_ max = 4 10^8 3.14 (4 10⁻³)^2 T_ max = 4 10^8 3.14 16 10⁻⁶ = 20096 N When the lift accelerates upwards with maximum acceleration a , the tension in the wire is: T_ max = m(g + a) 20096 = 1600(10 + a) 10 + a = 20096 1600 = 12.56 a = 12.56 - 10 = 2.56 m/s ^2 Answer: 2.56