Question

I'm not sure where to start. The drawing shows two crates that are connected by a steel wire that passes over a pulley. The unstretched length of the wire is 2.0 m, and its cross-sectional area is 1.6 *10^-5 [m^2]. The pulley is frictionless and massless. When the crates are accelerating, determine the change in length of the wire. Ignore the mass of the wire.

Answer 1

Attached is the image. Please help!

Answer 2

your goal is tension ?

Answer 3

Yes

Answer 4

Young's modulus of steel is 200gPa I think- how do I factor in the weight? I tried the usual deformation formula using 9.81*(m1+m2) as the force in newtons, but this does not yield the answer. I'm confused.

Answer 5

what is the cross sectional area means?

Answer 6

That is the area across the end of the wire, aka you cut the wire in half and its the area of the circle at the end of the wire.

Answer 7

oooo.. I think you should just search the tension by using the (sigma)F=ma for both crates, and just use the modulus young equation to search for the change of length

Answer 8

in which, Y=modulus young
F= the tension(in this case I think 2 times the rope's tension)
A = cross sectional area
l = the original length
(delta) l = the change of length

Answer 9

do you know relation of atwood acceleration & tesion ?
use from that

Answer 10

\[T=2m _{1}m _{2}g/m _{1}+m _{2}\]
for more see this:
http://en.wikipedia.org/wiki/Atwood_machine

Answer 11

did you get it?

Answer 12

Yes! Thank you!

Answer 13

your wellcome