Question

the aorta is a major artery, rising upward from the left ventricle of the heart and curving down to carry blood to the abdomen and lower half of the body. the curved artery can be approximated as a semicircular arch whose diameter is 5.5 cm. if blood flows through the aortic arch at a speed of 0.28 m/s, what is the magnitude (in m/s²) of the bloods centripetal acceleration?

Explanation:

Step1: Convert diameter to radius

First, convert the diameter $d = 5.5\ cm=0.055\ m$ to radius $r$. Since $r=\frac{d}{2}$, then $r=\frac{0.055}{2}= 0.0275\ m$.

Step2: Use centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $v = 0.28\ m/s$ and $r = 0.0275\ m$. Substitute the values: $a_c=\frac{(0.28)^{2}}{0.0275}=\frac{0.0784}{0.0275}\approx2.85\ m/s^{2}$.

Answer:

$2.85$