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A question from Gravitation.

Prince Patel Asked:

“Sun have high gravitational energy ,then why planets of solar system doesn’t colloid with sun?”

Answer:

“The planets are moving around the sun and the gravitational force is used in providing the necessary centripetal force (The force required by a body to move in a circular path). As long as the planets are in motion, they will not move towards the sun. A similar explanation hold good for moon going around earth also.”

Derive an expression for the minimum horizontal velocity to be given to a ball hanging vertically from a point so that it is able to just complete a vertical circular path.

While pushing, we are giving the ball some kinetic energy which will be converted to potential energy as it moves upward. If the whole kinetic energy is converted to potential energy at the top most point, it will fall straight down, resulting in only a semicircle. For the ball to continue the path, it should have a centrifugal force equal to weight of the body when it is at the topmost point.

let V be the initially applied velocity and v be the velocity at the topmost point

mv²/r = mg

v²/r = g

v² = rg

v = √(rg)

Potential Energy at the topmost point , Ep = 2mgr

Ep is the difference in kinetic energy between initial point(Ei) and at topmost point(Et).

                Ei – Et =  Ep

½mV² – ½mv² = 2mgr

      ½m(V²-v²) = 2mgr

            V²-v² = 4gr

                           V² = 4gr + v²

                          V² = 4gr + rg

                V² = 5rg

                  ========

A Problem from Gravitation

An artificial satellite is revolving around the earth in circular path at height equal to the radius of the earth.Find the speed of the satellite.The mass and radius of Earth are respectively 5.98 x 1024 kg and 6 x 103 km.

(Asked by Rehmat)

Answer:

Will be answered soon

CENTRIPETAL FORCE MISCONCEPTION

For a circular motion centripetal force is required. Is there any other force which could replace centripetal force to obtain a circular motion? (Asked Sajin)

Answer:

centripetal forcePlease note that Centripetal Force is the net force that must be acting towards the centre of the circular path. It may be provided by one or more of the forces of different kinds. It is not a kind of force like the frictional force or gravitational force. In different cases the centripetal force is provided by different forces.

For example, when we whirl a stone tied to the end of a rope in a horizontal plane, the tension in the string provides the centripetal force. Here the real force acting is the tension in the string and its magnitude equals the centripetal force mv^2/r.

Read more at the following links

  1. http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html
  2. http://en.wikipedia.org/wiki/Centripetal_force
  3. http://www.physicsclassroom.com/Class/circles/u6l1c.cfm

Why gravitational force of attraction is necessary for a satellite to revolve around earth?

The question was posted by Raj Kumar.

The satellite has a velocity. To revolve around, the direction of velocity must change. In the absence of a force it can move only in a straight line. It is the gravitational force which helps the satellite top change direction and revolve around the earth.

In other words, for a satellite to revolve in a circular path, a centripetal force is required. This centripetal force is provided by the force of gravitation only.

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