How Fast Must a Bacterium Cling to a Spinning Jet Tire?

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SUMMARY

The discussion focuses on calculating the rotational speed and forces acting on a bacterium clinging to a spinning jet tire. The tire's diameter is 0.850 m, leading to a radius of 0.425 m. The tire rotates at approximately 224.4 rpm, with a centripetal acceleration of 8,400 m/s² at the edge. A bacterium weighing 10^-15 kg must exert a cling force equal to its mass multiplied by the centripetal acceleration, resulting in a force of 7.0 x 10^-12 N, which is significantly greater than its weight.

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  • Understanding of angular velocity and its calculation
  • Knowledge of centripetal acceleration and its formula
  • Basic principles of force and mass in physics
  • Familiarity with unit conversions, particularly between linear and rotational measurements
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  • Learn about the relationship between linear velocity and angular velocity in rotating systems
  • Study the concept of centripetal force and its applications in real-world scenarios
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  • Investigate the dynamics of small organisms in high-speed environments
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Students in physics, particularly those studying mechanics, as well as anyone interested in the dynamics of small organisms in motion, such as microbiologists and aerospace engineers.

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Homework Statement


At takeoff, a commercial jet has a speed of 60.0 m/s. Its tires have a diameter of
0.850 m.
(a) At how many rpm are the tires rotating?
(b) What is the centripetal acceleration at the edge of the tire?
(c) With what force must a determined 10-15 kg bacterium cling to the rim?
(d) What is the ratio of this force to the bacterium’s weight?


Homework Equations


angular velocity = v/r
centripetal acceleration = v^2/r


The Attempt at a Solution



I divided 60.0 m/s by .425 m to get (a). To get (b) I squared 60.0 m/s and divided it by .425 m. I am really stuck on (c). I am thinking the force it needs to cling to the rim is equal to the centripetal force. So, does that mean I just multiple it's mass by the centripetal acceleration? Any help would be appreciated.
 
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Take care with the answer to (a). v/r is the angular velocity, not the revolutions per minute, rpm.
(c): you are right, the centripetal force is centripetal acceleration multiplied by the mass and that force is needed to move together with the tyre.

ehild
 

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