A community for students.
Here's the question you clicked on:
 0 viewing
mortonsalt
 one year ago
A fine steel wire is attached to an aluminum cylinder in parallel (see picture I'll attach below). The structure is assembled at 10.0°C under negligible stress. The initial length of the system is
85.0 cm long.
The system is heated to 120°C. Calculate the resulting stress in the wire, assuming that
the rod expands freely. Justify the assumption that the rod freely expands.
mortonsalt
 one year ago
A fine steel wire is attached to an aluminum cylinder in parallel (see picture I'll attach below). The structure is assembled at 10.0°C under negligible stress. The initial length of the system is 85.0 cm long. The system is heated to 120°C. Calculate the resulting stress in the wire, assuming that the rod expands freely. Justify the assumption that the rod freely expands.

This Question is Closed

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443935742152:dw

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Is the strain on the Al rod as it expands equal to the stress on the steel wire?

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Or do I use the formula \[\frac{F}{A} = Y \alpha \Delta T\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3I think that we can assume that rod can expand freely since Aluminum is more sensible to temperature than steel, here are the values of linear expansion coefficients: Al> 23.6 Steel (Fe)> 11.7 the units are \(10^{7} K^{1}\)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3oops.. the units are: \(10^{6} K^{1}\)

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Firstly, thank you! :) Is there any way I can use that information to calculate the resulting stress on the wire?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3we can compute the unitary stress, namely force over cross section of wire, using this formula: \[\sigma = \alpha \cdot \Delta t \cdot E\] where \(\alpha\) is the linear expansion coefficient of steel, \(\Delta t\) is the change of temperature, and \(E\) is the Young modulus, namely the same as your formula above

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3of corse \(E\) is the Young modulus of steel

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Alright. Here are my thoughts: The rod will expand faster than the wire. Is there another force pulling at the wire from the expansion of the rod? If so, would it affect how much stress is applied on the rod?

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, how much stress is applied on the wire*

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3I think that we have to consider the weight of the wire, nevertheless it can be considered negligible in comparison with the unitary stress \(\sigma\)

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Would that be it then? I just have to plug in the values into the formula for unitary stress?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3yes! I think so!

mortonsalt
 one year ago
Best ResponseYou've already chosen the best response.0Alrighty! Thanks for the input!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.