[填空题]
A rectangle was drawn using a ruler, such thasgpl( b48e nepk+r5f /q)lni/t each measurement p xi7os 2dl0w:1naw7fhas an uncertainty filw 0xopwa72:s1 7dnof $0.5 \mathrm{~cm} .$
What is the absolute uncertainty in the area of the entire rectangle (i.e. combined small and big rectangles), in $\mathrm{cm}^2$ ? $cm^2$ (please only input numerical value without units and without the $\pm$ symbol.)
参考答案: 11
本题详细解析: The sides of the rec5 i9(c:v66 xsj-/gd n zvxnakhtangle are $(5.0 \pm 0.5) \mathrm{cm}$ and $(12.0 \pm 1.0) \mathrm{cm}$. Note that the length of the long side of the rectangle is calculated using two separate length calculations, each with an uncertainty of $\pm 0.5 \mathrm{~cm}$, giving a total uncertainty of $\pm 1.0 \mathrm{~cm}$ for that side.
The fractional uncertainty on the area will be:
$\frac{\Delta A}{A}=\frac{0.5}{5.0}+\frac{1.0}{12.0}=0.18$
The area of the rectangle is:
$A=5.0 \times 12.0=60 \mathrm{~cm}^2$
so the absolute uncertainty on the area is:
$\Delta A=0.18 \times 60=11 \mathrm{~cm}^2$
Post time 2024-8-21 21:38:19
