Physics 12.7 ex no. 3 help!!!!

Question

The length of a steel beam increases by 0.79mm when its temperature is raised

from 22 degrees C to 35 degrees C. What is the length of the beam at 22 degrees C?

Answer 1

L + 0.00000645*(9/5)*13*L = L+0.79

0.00000645*(9/5)*13*L = L+0.79 -L

0.00000645*(9/5)*13*L = 0.79

L = 0.79/(0.00000645*(9/5)*13)

L=0.79 / (0.00000645 * (9 / 5) * 13) = 5 234.21454 mm = 5.234 m

this was supposed to go below the 3 links.

y/a wouldn't let me post it.

i've no idea why.

(.00000645 * 9) / 5 = 1.16100 × 10-5 <== first link = used

Steel, depends on composition 11.0 ~ 13.0 <== 3rd link

note, the first link is in Fahrenheit. the 9/5 converts it to centigrade.

Answer 2

L = Lo + delta L

L = Lo + (Lo)(alpha)(delta T)]

where

L = length of the steel any temperature

Lo = original length of the steel at 22 degrees

delta L = change in length of steel = 0.79 mm (given)

alpha = coefficient of linear expansion of steel = 13.2 x 10^-6

delta T = 35 - 22 = 13

NOTE that the increase in length

(L - Lo) = 0.79 mm = Lo(alpha)(delta T)

Substituting appropriate values,

0.79 = Lo(13.2 x 10^-6)(13)

Solving for Lo,

Lo = 0.79/[(13.2 x 10^-6)(13)]

Lo = 4603.73 mm

Answer 3

Thermal deformation = alpha*delta T*L

alpha = coefficient of thermal expansion (stainless steel's is 17.3 *10^(-6) in/deg C at 20 deg C so convert to mm before you use it and cite that you assumed that value)

delta T is the change in temp

L is the original length

Use .79 mm = alpha * (35-22) * L and solve for L

Edit: Meh I'm bored I'll do it

alpha = 0.00043942 millimeters/deg C

solving for L gives 138.294185 mm, (check the units)