Posted by jo on .
Here were two tricky questions. Please provide steps. Answers are not necessary (since these are practice questions for an exam).
1.) The centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance to cause the more less dense blood serum and collect at the bottom. The question is suppose the centripetal Acceleration is 6.5*10^3 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 5.00 cm from axis of rotation?
2.)A penny is placed at the outer edge of a disk with radius = 0.150m. that rotates about an axis perpendicular to the plane of the disk at its center. The period is 1.8 seconds. Find the minimum coeficient of friction necessary to allow the penny to rotate along with the disk.
I have a general idea of how to do the first one.. so I'll provide the necessary equations. a = v^2/r, and 2(pie)r/v. I will be bumping this thread accordingly.
1) Solve this equation for angular velocity w (radians per second), then convert w to rpm
R*w^2 = 6500*g
R = 0.05 m.
g = 9.8 m/s^2
w = sqrt[6500(g/R)]
2. Let U be the coefficient of syatice friction
M g U = M Rw^2
U = R w^2/g
If the period is P = 1.8 s,
w = 2 pi/P = 3.49 rad/s
a. a= 6500*9.8m/s
a= w^2/r solve for w
w is in radians/second, so you have to change that to rev/min (1/(2PI*60)
centripetal force wants requires the following force to keep it in place
but friction to provide this is mu*mg
solve for mu