Problem Set 10

Physics 5200

Due 20 Apr. 1999

1. (2 points) An ultracentrifuge is a device commonly used to separate biomedical samples, for instance to separate red blood cells from blood plasma. If an ultracentrifuge rotates with a speed of 500 rotations per second (rps),
   1. find the centrifugal force on a 1mg particle in the sample if the particle is 5cm from the rotational axis, and
   2. express the result as the ratio of the centrifugal force to the weight of the particle.
      
      
2. (3 points) A truck, initially at rest, has its rear door fully open, as shown. The truck accelerates forward at constant rate A, and the door begins to swing shut. The door is uniform and solid, of total mass M, height h, and width w. (Neglect air resistance.) Find the instantaneous angular velocity of the door about its hinge when it has swung through 90°. Hint: Consider the problem in the truck's frame of reference. Then the door rotates on a fixed axis, and the techniques of chapter 8 can be applied. Also note that you may find it helpful to transform a time derivative to an angular derivative as: dw/dt = (dw/dq)(dq/dt) = w dw/dq = 1/2 dw²/dq .
   
   
   
   
   
   
   
   
   
   
   
3. (3 points) A coackroach crawls with constant speed in a circular path or radius b on a phonograph turntable rotating with constant angular speed w. The circular path is concentric with the center of the turntable. if the mass of the insect is m and the coefficient of static friction with the surface of the turntable is m_s, how fast, relative to the turntable, can the cockroach crawl before it starts to slip if it goes
   1. in the direction of rotation and
   2. opposite to the direction of rotation?
      
      

4. (2 points) Show that, for an object moving horizontally on the surface of the Earth, the magnitude of the horizontal component of the Coriolis force is independent of the direction of the motion of the particle. Horizontal means parallel to the surface at the object's location.