Youngs modulus?

Question

I need to work out the extension of a steel cable holding a lift that weighs 900kg, gravity is to be based at 10ms2 and the cable is 9m long and has a diameter of 10mm the youngs modulus of the cable is 210GNm2 can you help?
Its very easy but i dont know wat i am doing wrong

Answer 1

Deforming force,F= 900 kg wt= 900*g=900*10=9000 newton

Length of cable L = 9 m

radius of cable 'r' = diameter/2 =10 mm/2=5 mm=5*10^ -3 m

Young's modulus of steel Y =210 G Nm^- 2= 2.1*10^11 Nm^ -2

Extension of cable 'l'= ?

Y=[stress /strain]=[ F/pi r^2] / [l /L]

=[F L / (pi r^2)*l]

extension l =F L /(pi r^2)* Y


= 9000*9 / 3.14*5*10^-3*5*10^-3*2.1*10^11

=4.91*10^ -3= 4.91 mm

Answer 2

YM=Stress/Strain

Stress =F/A
F=mg
A=(piD^2)/4

Strain = extent ion / length

so Strain=Stress / YM

extension=Strain x length
extension= Stress length / YM

extension= (4 m g / (pi D^2)) ength / Ym
extension = ( 4 x 900 x 10 / (3.14159.. (0.01)^2)/210 E+9 N m^2)
extension= 5.46 E-4m or
extension= .546 mm

Answer 3

LD is spot on. another piece of information - in case you do a YM test attempt utilising a organic copper cord. in case you get "creep" IE the steel looks to strech below its own weight very slowly think ofyou've have been given a solid set-up. additionally for extra accuracy you additionally could make a dial. you will want some pins and rather some somewhat stiff cardboard. placed one pin in a weighted corron reel to apply as a pivot. superglue yet another pin a million meter out of your tie factor on you cord below try. Make a protracted skinny piece of cardboard approximately 5mm by utilising 230mm and precisely 200mm from one end placed the pin with the aid of and into the cotton reel )then placed a small mark on the top of the long end). that's your pivot factor. circulate this into alignment so as that the 30mm end is in touch with the pin on your cord 20mm faraway from the pivot pin. the different long end could desire to be resting on a ruler and ideally your piece of cardboard ought to be at a great attitude to the cord being measured. That set up can supply the equivalent of utilising a sprint cord ten circumstances longer than you genuinely use and therefor if used properly improves your accuracy by utilising one decimal place. i became into assuming you in basic terms had room for a a million meter set-up yet once you will get a 10 meter set-up do it and use the pivot rig. That way you're transforming into to be the equivalent of one hundred meters.