As a result of a temperature rise of 37 Co, a bar with a crack at its center buckles upward (see the figure). If the fixed distance Lo is 4.35 m and the coefficient of linear expansion of the bar is 25.0 x 10-6/c°, find the rise x of the center. Lo L. 0 Numbert 0402 unit-t Units m the tolerance is +/-1 in the 3rd significant digit
Solution
New length of the bar,
L = Lo + Lo*alfa*dT
= 4.35 + 4.35*25*10^-6*37
= 4.35402375
from figure, using pythogorous theorem,
(L/2)^2 = (Lo/2)^2 + x^2
x^2 = (L/2)^2 - (Lo/2)^2
x = sqrt((L/2)^2 - (Lo/2)^2)
= sqrt((4.35402375/2)^2 - (4.35/2)^2)
= 0.093572 m
= 0.936 m (when rounded to three significant figures)
.
As a result of a temperature rise of 37 Co- a bar with a crack at its.docx
1. As a result of a temperature rise of 37 Co, a bar with a crack at its center buckles upward (see the
figure). If the fixed distance Lo is 4.35 m and the coefficient of linear expansion of the bar is
25.0 x 10-6/c°, find the rise x of the center. Lo L. 0 Numbert 0402 unit-t Units m the tolerance
is +/-1 in the 3rd significant digit
Solution
New length of the bar,
L = Lo + Lo*alfa*dT
= 4.35 + 4.35*25*10^-6*37
= 4.35402375
from figure, using pythogorous theorem,
(L/2)^2 = (Lo/2)^2 + x^2
x^2 = (L/2)^2 - (Lo/2)^2
x = sqrt((L/2)^2 - (Lo/2)^2)
= sqrt((4.35402375/2)^2 - (4.35/2)^2)
= 0.093572 m
= 0.936 m (when rounded to three significant figures)
