Question

A 2.8 meter wire with square cross section of 1.2 mm by 1.2 mm stretched 1.43 mm when it supported a 17 kg mass. Cut a length of this wire 0.28 m long and hang a 17 kg mass from it. How much will this short wire stretch, in millimeters? stretch = mm

Answer 1

Answer:0.143 mm

Step-by-step explanation:

Given

Length of wire
`L=2.8\ m`

Cross-section of wire
`A=1.2* 1.2\ mm^2`

Extension in wire on application of load
`\delta L=1.43\ mm`

Mass of support
`m=17\ kg`

Weight of support
`W=mg=17* 9.8=166.6\ N`

Extension in the wire is given by

`\delta L=(PL)/(AE)`

where E=Young's Modulus

substitute values

`1.43=(166.6* 2.8)/(1.44* E)----1`

When wire is cut for length of
`L'=0.28\ m`

extension is given by

`\delta L'=(166.66* 0.28)/(1.44* E)---2`

divide 1 and 2 we get

`(1.43)/(\delta L')=(2.8)/(0.28)`

`\delta L'=0.143\ mm`