Mech of Materials stretching wire problem

[koab1mjr]

Homework Statement

The length of a 2mm diameter steel wire CD has been adjusted so that with no load applied a gap of 1.5mm exists between end B of the rigid beam ACB and a contact point E. Knowing E = 200GPa, determine where the 20kg block should be placed on the beam in order to cause contact between B and E

http://tinypic.com/r/11lnexu/6
http://uploading.com/files/388fce7c/hwprob.png/

Homework Equations

Summation of Forces
Deformation = Load*Lenght/ Area*Modulus of Elasiticty
slope of a line

The Attempt at a Solution

My approach is as follows, first see how far the wire must stretch to allow the beam to become in contact with the surface. Since the Beam is rigid it must form a straigth line and using that knowledge I found that the wire must elongate by .3mm. With that information I was going to plug the deformation and solve for force which gave me a large number of 753N required to stretch the wire that much...

Now my problems begin. I have reaction at A due to the pin and 20kg box which results in a 196N force. So with a force balance in the Y axis I can find all the forced but this where I am stuck how do I find out where the box go. Why does it matter? I am not sure how the moment plays a role but I know that must be the key. Am I supposed to find the position whichs moments are all zero? I am not sure how the placement affects this question since the elongation is driven by the axial load.

I am supposed to be solving for x to place the block. I feel confident about the elogation and hence the force required on the wire. From there I need a push to finish this

Any help is much appreciated

 

[PhanthomJay]

Homework Statement

The length of a 2mm diameter steel wire CD has been adjusted so that with no load applied a gap of 1.5mm exists between end B of the rigid beam ACB and a contact point E. Knowing E = 200GPa, determine where the 20kg block should be placed on the beam in order to cause contact between B and E

http://tinypic.com/r/11lnexu/6
http://uploading.com/files/388fce7c/hwprob.png/

Homework Equations

Summation of Forces
Deformation = Load*Lenght/ Area*Modulus of Elasiticty
slope of a line

The Attempt at a Solution

My approach is as follows, first see how far the wire must stretch to allow the beam to become in contact with the surface. Since the Beam is rigid it must form a straigth line and using that knowledge I found that the wire must elongate by .3mm.

yes, very good

With that information I was going to plug the deformation and solve for force which gave me a large number of 753N required to stretch the wire that much...

I can't do the math (too many decimals when using SI), but I assume that you used T= AE(delta)/L. so I'll take your word for it that T =753 N:yuck:

Now my problems begin. I have reaction at A due to the pin and 20kg box which results in a 196N force.

The reaction force at A is equal to T -196, acting downward on the beam, using Newton 1

So with a force balance in the Y axis I can find all the forced but this where I am stuck how do I find out where the box go. Why does it matter? I am not sure how the moment plays a role but I know that must be the key. Am I supposed to find the position whichs moments are all zero?

Yes! Sum moments about any point = 0 to solve for x.

I am not sure how the placement affects this question since the elongation is driven by the axial load.

yes, now you must find where the load must be placed to produce that axial load, by summing moments about any point =0

I am supposed to be solving for x to place the block. I feel confident about the elogation and hence the force required on the wire. From there I need a push to finish this

Any help is much appreciated

Push on! You've done quite well so far.

 

[koab1mjr]

ok thanks for your help i was able to finish the problem