A thin, circular ring B (mass m, radius r) is placed in the gravitational field of aparticle P (mass M). Unit vectors ô are fixed in the ring and the ring is uniform. The unit vectorbis directed from P to the ring center of mass B* and is normal to the ring plane. Let r = .75 R.Determine the exact gravity force on B due to P. (You can integrate with a thin ring!!)Use this F and locate the c.g.exact Mark its relative location on the sketch.exactb₂DB*b,RP (M)

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Determine the exact gravity force on B due to P. (

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

A thin, circular ring B (mass m, radius r) is placed in the gravitational field of a
particle P (mass M). Unit vectors ô are fixed in the ring and the ring is uniform. The unit vector
bis directed from P to the ring center of mass B* and is normal to the ring plane. Let r = .75 R.
Determine the exact gravity force on B due to P. (You can integrate with a thin ring!!)
Use this F and locate the c.g.exact Mark its relative location on the sketch.
exact
b₂
D
B*
b,
R
P (M)

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Step 1: Draw the small elemental mass dm on the ring and distance x between mass dm and M.

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Step 2: Calculate the mass of small element on the ring in terms of small angle.

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Step 3: Write the gravity force equation between mass dm and mass M.

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Step 4: Integrate the equation for complete circular ring from 0 to 2pi.

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Step 5: Locate the Centre of gravity.

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