An ultracentrifuge is a laboratory instrument where tubes containing samples are rotated at high speed around a vertical axis. You are tasked with designing an ultracentrifuge capable of producing an apparent gravity of 5 x 105g at r = 0.2m from the axis of rotation. Assume that in the steady state the sample tubes are oriented horizontally, that g = 10m/s2, and that regular gravity may be ignored. (a) How fast should the rotor housing the sample tubes spin? (b) A particle in one of the sample tubes is moving outward with radial speed v, = 0.1m/s, towards the bottom of the tube. Does an extra force appear due to this motion? If so, give the direction and magnitude of the force. If not, explain why there is no extra force. Do your results depend on how far from the axis of rotation the particle is?

An ultracentrifuge is a laboratory instrument where tubes containing samples are rotated at high speed around a vertical axis. You are tasked with designing an ultracentrifuge capable of producing an apparent gravity of 5 x 105g at r = 0.2m from the axis of rotation. Assume that in the steady state the sample tubes are oriented horizontally, that g = 10m/s2, and that regular gravity may be ignored. (a) How fast should the rotor housing the sample tubes spin? (b) A particle in one of the sample tubes is moving outward with radial speed v, = 0.1m/s, towards the bottom of the tube. Does an extra force appear due to this motion? If so, give the direction and magnitude of the force. If not, explain why there is no extra force. Do your results depend on how far from the axis of rotation the particle is?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Gravitational force

In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.

Acceleration Due to Gravity

In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

Question

Question 4.

(d) What is the criterion for stability if the potential is V(r) = -(A/r)e-r/a?
4. An ultracentrifuge is a laboratory instrument where tubes containing samples are rotated at high speed around a
vertical axis. You are tasked with designing an ultracentrifuge capable of producing an apparent gravity of 5 x 105g
at r = 0.2m from the axis of rotation. Assume that in the steady state the sample tubes are oriented horizontally,
that g=10m/s2, and that regular gravity may be ignored.
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(a) How fast should the rotor housing the sample tubes spin?
(b) A particle in one of the sample tubes is moving outward with radial speed v, = 0.1m/s, towards the bottom of
the tube. Does an extra force appear due to this motion? If so, give the direction and magnitude of the force.
If not, explain why there is no extra force. Do your results depend on how far from the axis of rotation the
particle is?
5. A cannon is placed on the surface of the Earth at colatitude (polar angle) and pointed due east. The cannon barrel
makes an angle a with the horizontal, and the projectile emerges with initial speed vo. The rotational speed of the
Earth around its polar axis is w. (Hints: use the expansion r(t) = Fo(t) + ri(t) in powers of w; use a coordinate
sustem with anointina South along the surface. û nointina East along the surface. and 2 pointing un perpendicularly
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Step 1: Determine the given data:

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Step 2: a) Determine the rotational speed:

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Step 3: b) Explain the force on the moving particle:

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