a certain centrifuge produce a centripetal acceleration of magnigtude exactly 1410g at a point 12.3 cm from the axis of rotation. find the number of revolutions per second
To find the number of revolutions per second, we need to use the formula for centripetal acceleration, which is given by:
ac = (v^2) / r
Where:
- ac is the centripetal acceleration
- v is the velocity of the object
- r is the distance from the axis of rotation
In this case, we are given the magnitude of the centripetal acceleration (1410g) and the distance from the axis of rotation (12.3 cm).
To start, we need to convert the distance from centimeters to meters. We can do this by dividing the given distance by 100:
r = 12.3 cm / 100 = 0.123 m
Next, we need to convert the magnitude of the centripetal acceleration from gravitational units (g) to meters per second squared (m/s^2). We know that 1 g is equal to 9.8 m/s^2:
ac = 1410 g * 9.8 m/s^2 = 13818 m/s^2
Now, we can rearrange the formula to solve for the velocity (v):
v = sqrt(ac * r)
v = sqrt(13818 m/s^2 * 0.123 m) ≈ 14.402 m/s
Finally, to find the number of revolutions per second, we need to divide the velocity by the circumference of the circular path. The circumference is given by:
C = 2 * π * r
C = 2 * π * 0.123 m ≈ 0.772 m
Now, we can calculate the number of revolutions per second (f):
f = v / C
f = 14.402 m/s / 0.772 m ≈ 18.665 revolutions/second
Therefore, the number of revolutions per second is approximately 18.665.