Each of the space shuttle's main engines is fed liquid hydrogen by a high-pressure pump. Turbine blades inside the pump rotate at 595 rev/s. A point on one of the blades traces out a circle with a radius of 0.02 m as the blade rotates.
(a) What is the magnitude of the centripetal acceleration that the blade must sustain at this point?
1 m/s2
(b) Express this acceleration as a multiple of g = 9.80m/s2.
To find the magnitude of the centripetal acceleration, we can use the formula:
ac = ω^2 * r
Where:
ac = centripetal acceleration
ω = angular velocity (in radians per second)
r = radius
(a) First, we need to convert the given angular velocity from revolutions per second (rev/s) to radians per second (rad/s).
1 revolution = 2π radians
So, the angular velocity in radians per second is given by:
ω = 595 rev/s * 2π rad/rev
= 595 * 2π rad/s
Next, we can substitute the values into the formula to calculate the centripetal acceleration:
ac = (595 * 2π rad/s)^2 * 0.02 m
≈ 707.88 m/s^2
Therefore, the magnitude of the centripetal acceleration that the blade must sustain is approximately 707.88 m/s^2.
(b) To express this acceleration as a multiple of g = 9.80 m/s^2, we divide the centripetal acceleration by the acceleration due to gravity:
Multiple of g = ac / g
= 707.88 m/s^2 / 9.80 m/s^2
≈ 72.25
Hence, the expression of the centripetal acceleration as a multiple of g is approximately 72.25 times g.