Deformation of solids

[winnie101]

could someone plz explain howto do the following ques
a) the steel cable on a crane has a diameter of 13mm. what force is necessary to produce srain of 0.1% in the wire?
b) what is the maximun acceleration with which it can lift a load of mass 1000kg if the strain in the cable is not to exceed 0.1%. the young modulus of the high-tension steel used is 2.4x10^11 pa

[astarmathsandphysics]

Will have to do this when I get home

[godfather93]

the steel cable on a crane has a diameter of 13mm. what force is necessary to produce srain of 0.1% in the wire?

Ans:  Young's mod= stress/strain = force/(area*strain)= (2.40*10^11) / (pi * ((13 * 10^-6) / 2)^2  * 0.001)


what is the maximum acceleration with which it can lift a load of mass 1000kg if the strain in the cable is not to exceed 0.1%.

Young's mod = Force / (Area*strain)
But Force = mass * acceleration from Newton's second law of motion, so

Y = (mass*acceleration) / (Area*strain)

Rearranging we get

m = (Y * Area * strain) / mass