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william313
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Hello. I have this easy question in linear expansion. Yeah, it's easy but I am really dumb in physics. Please help..
Rod A which is 30 cm long, expands by 0.045 cm when heated from 0 degrees Celsius to 100 degrees Celsius. Rob B also 30 cm long expands by 0.075 cm for the same change in temperature. Rod C, also 30 cm long is made up of the materials of Rod A and B, connected end to end. It expands by 0.065 cm when heated from 0 degrees Celsius to 100 degrees Celsius. Calculate the initial lengths of rods A and B in C.
given:
Initial length of A = 30 cm
Change in length of A = 0.045 cm
Initial length of B = 30 cm
Change in length of B = 0.075 cm
Initial length of C = 30 com
Change in length of A = 0.065 cm
Change in temperature = 100 degrees Celsius (100 - 0)
Initial length of Rod A in Rod C = ?
Initial length of Rod B in Rod C = ?
Coefficient of linear expansion = change in length / (initial length x change in temperature)
My strategy is:
- get the coefficient of linear expansion of rods A and C.
- get the percentage of the coefficient of linear expansion of Rod A from Rod C.
- get the value of the change in length of A base on the percentage.
- solve for initial length of Rod A base on the formula given above.
- deduct the initial length of Rod C from the initial length of Rod A to get Rod B's initial length.
solution:
let Li be the initial length. Lia for initial length of rod a, Lib for rod b and Lic for rod c.
let cL be the change in length. cLa for rod a, clb for rod b and cLc for rod c.
let C be the coefficient of linear expansion. Ca for rod a and Cc for rod c
let t be the change in temperature.
C = cL / Li x t
Ca = cLa / Lia x t
Ca = 0.045 cm / 30 cm (100)
Ca = 1.5 x 10-5
Cc = cLc / Lic x t
Cc = 0.065 cm / 30 cm (100)
Cc = 2.167 x 10-5
get the percentage of rod a from rod c base on the coefficient of linear expansion:
= 1.5 x 10-5 / 2.167 x 10-5
= 0.69
cLa in rod c = 0.065 (.69)
cLa in rod c = 0.045
Lia in rod c = cLa in rod c / Ca x t
Lia in rod c = 30 cm
Lib in rod c = 30 cm - 30 cm
Lib in rod c = 0
As you can see. my attempted solution is obviously an error. Please help. Do you guys know how to answer this?
Homework Statement
Rod A which is 30 cm long, expands by 0.045 cm when heated from 0 degrees Celsius to 100 degrees Celsius. Rob B also 30 cm long expands by 0.075 cm for the same change in temperature. Rod C, also 30 cm long is made up of the materials of Rod A and B, connected end to end. It expands by 0.065 cm when heated from 0 degrees Celsius to 100 degrees Celsius. Calculate the initial lengths of rods A and B in C.
given:
Initial length of A = 30 cm
Change in length of A = 0.045 cm
Initial length of B = 30 cm
Change in length of B = 0.075 cm
Initial length of C = 30 com
Change in length of A = 0.065 cm
Change in temperature = 100 degrees Celsius (100 - 0)
Initial length of Rod A in Rod C = ?
Initial length of Rod B in Rod C = ?
Homework Equations
Coefficient of linear expansion = change in length / (initial length x change in temperature)
The Attempt at a Solution
My strategy is:
- get the coefficient of linear expansion of rods A and C.
- get the percentage of the coefficient of linear expansion of Rod A from Rod C.
- get the value of the change in length of A base on the percentage.
- solve for initial length of Rod A base on the formula given above.
- deduct the initial length of Rod C from the initial length of Rod A to get Rod B's initial length.
solution:
let Li be the initial length. Lia for initial length of rod a, Lib for rod b and Lic for rod c.
let cL be the change in length. cLa for rod a, clb for rod b and cLc for rod c.
let C be the coefficient of linear expansion. Ca for rod a and Cc for rod c
let t be the change in temperature.
C = cL / Li x t
Ca = cLa / Lia x t
Ca = 0.045 cm / 30 cm (100)
Ca = 1.5 x 10-5
Cc = cLc / Lic x t
Cc = 0.065 cm / 30 cm (100)
Cc = 2.167 x 10-5
get the percentage of rod a from rod c base on the coefficient of linear expansion:
= 1.5 x 10-5 / 2.167 x 10-5
= 0.69
cLa in rod c = 0.065 (.69)
cLa in rod c = 0.045
Lia in rod c = cLa in rod c / Ca x t
Lia in rod c = 30 cm
Lib in rod c = 30 cm - 30 cm
Lib in rod c = 0
As you can see. my attempted solution is obviously an error. Please help. Do you guys know how to answer this?