How do you solve this problem?
How fast (in rpm) must a centrifuge rotate if a particle 9.00cm from the axis of rotation is to experience an acceleration of 115,000 g's?
115000g=w^2 * r
you know g, r, solve for w (in radians per second). Convert that to rpm
I am confused, can someone show me how to work this problem? I really need help!
How do you work this problem out??
To solve this problem, we need to use the centripetal acceleration formula. The formula for centripetal acceleration is given by:
a = (ω^2) * r
where 'a' is the centripetal acceleration, 'ω' is the angular velocity (in radians per second), and 'r' is the distance from the axis of rotation.
In this problem, the acceleration is given as 115,000 g's. Since 1 g is equal to 9.8 m/s^2, we can convert 115,000 g's to meters per second squared:
a = 115,000 g's * 9.8 m/s^2 = 1,127,000 m/s^2
The distance 'r' is given as 9.00 cm. Since we need 'r' in meters, we convert it to meters by dividing by 100:
r = 9.00 cm / 100 = 0.09 m
Now we can rearrange the formula to solve for angular velocity:
ω = √(a / r)
Substituting the given values:
ω = √(1,127,000 m/s^2 / 0.09 m) = √(12,522,222,222.22) ≈ 111,810 rad/s
Finally, to convert from radians per second to rotations per minute (rpm), we need to multiply by a conversion factor. There are 2π radians in one revolution, and 60 seconds in one minute, so:
1 rad/s = (1/(2π)) revolutions per second
1 revolution per minute (rpm) = 60/(2π) rad/s
Multiplying our angular velocity by the conversion factor:
111,810 rad/s * (60/(2π)) = 1,064,772 rpm
Therefore, the centrifuge must rotate at approximately 1,064,772 rpm in order for a particle located 9.00 cm from the axis of rotation to experience an acceleration of 115,000 g's.