The curved artery can be approximated as a semicircular arch whose diameter is 4.9 cm. If blood flows through the aortic arch at a speed of 0.35 m/s, what is the magnitude (in m/s2) of the blood's centripetal acceleration?
d= 4.9 which means r=2.45cm. change that to meters, 0.0245m.
v=0.35
a=v^2/r
a=(o.35^2)/0.0245
To find the magnitude of the blood's centripetal acceleration, we need to first understand the formula for centripetal acceleration.
The formula for centripetal acceleration is given by:
a = (v^2) / r
where:
a is the centripetal acceleration
v is the velocity of the blood
r is the radius of the curved artery
Given:
v = 0.35 m/s
r = (diameter of the artery) / 2 = 4.9 cm / 2 = 2.45 cm = 0.0245 m
Substituting these values into the formula, we get:
a = (0.35^2) / 0.0245
Calculating this, we find:
a = 5.025 m/s^2
Therefore, the magnitude of the blood's centripetal acceleration is approximately 5.025 m/s^2.
To find the magnitude of the blood's centripetal acceleration, we need to use the formula:
ac = v^2 / r
Where:
ac is the centripetal acceleration
v is the velocity of the blood flow
r is the radius of the semicircular arch
In this case, the diameter of the semicircular arch is given, so we first need to find the radius:
radius = diameter / 2 = 4.9 cm / 2 = 2.45 cm
Next, we need to convert the radius to meters since the velocity is given in meters per second:
radius = 2.45 cm * 0.01 m/cm = 0.0245 m
Now we can substitute the given values into the centripetal acceleration formula:
ac = (0.35 m/s)^2 / 0.0245 m
Calculating this expression gives us:
ac = 0.1225 m^2/s^2 / 0.0245 m
Simplifying further:
ac = 5 m^2/s^2
Thus, the magnitude of the blood's centripetal acceleration is 5 m/s^2.