Physics Complete: Gravitation

Showing posts with label Gravitation. Show all posts

Weightlessness

Weight of an object is the force with which the earth attracts it. We are conscious of our own weight when we stand on a surface, since the surface exerts a force opposite to our weight to keep us at rest.

The same principle holds good when we measure the weight of an object by a spring balance hung from a fixed point e.g. the ceiling. The object would fall down unless it is subject to a force opposite to gravity. This is exactly what the spring exerts on the object. This is because the spring is pulled down a little by the gravitational pull of the object and in turn the spring exerts a force on the object vertically upwards.

Imagine that the top end of the balance is no longer held fixed to the top ceiling of the room. Both ends of the spring as well as the object move with identical acceleration g. The spring is not stretched and does not exert any upward force on the object which is moving down with acceleration g due to gravity.

The reading recorded in the spring balance is zero since the spring is not stretched at all. If the object were a human being, he or she will not feel his weight since there is no upward force on him. Thus, when an object is in free fall, it is weightless and this phenomenon is usually called the
phenomenon of weightlessness.

In a satellite around the earth, every part and parcel of the satellite has an acceleration towards the center of the earth which is exactly the value of earth’s acceleration due to gravity at that position. Thus in the satellite everything inside it is in a state of free fall. This is just as if we were falling towards the earth from a height.

Thus, in a manned satellite, people inside experience no gravity. Gravity for us defines the vertical direction and thus for them there are no horizontal or vertical directions, all directions are the same. Pictures of astronauts floating in a satellite reflect show this fact.

Related posts :

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Sign Convention and Image Tracing of Light in Ray Optics

Problems and Solutions on Refraction of Light

Refraction of Light and Snell's Law

Problems and solutions on Refraction of Light

Normal Shift and Lateral Shift due to Refraction of Light

Problems on normal shift Refraction of Light

Gravitational Potential Energy
Universal Gravitational constant
Kepler laws of gravitation

Gravitational Potential Energy

Gravitational potential energy is the energy possessed by the by virtue of its position on the surface of earth.

It is the work done in bringing the unit positive charge from infinite distance to a particular point.

Potential energy is the energy stored in the body at its given position. If the position of the particle changes on account of forces acting on it, then the change in its potential energy is just the amount of work done on the body by the force.

Forces for which the work done is independent of the path are the conservative forces. The force of gravity is a conservative force and the potential energy of a body arising out of this force, called the gravitational potential energy.

If points close to the surface of earth, at distances from the surface much smaller than the radius of the earth, the force of gravity is practically a constant equal to mg, directed towards the center of the earth.

If we consider a point at a height h1 from the surface of the earth and another point vertically above it at a height h2 from the surface, the work done in lifting the particle of mass m from the first to the second position is

W12 = Force × displacement = mg (h2 – h1).

If we associate a potential energy W(h) at a point at a height h above the surface such that
W(h) = mgh + Wo (where Wo = constant) ;

Then it is clear that W12 = W(h2) – W(h1)

The work done in moving the particle is just the difference of potential energy between its final and initial positions.

The constant Wo cancels out in the above Eq.

Setting h = 0 in the equation, we get W ( h = 0 ) = Wo. h = 0 means points on the surface of the earth. Thus, Wo is the potential energy on the surface of the earth.

Ray Optics Introduction and Reflection of Light

Sign Convention and Image Tracing of Light in Ray Optics

Problems and Solutions on Refraction of Light

Refraction of Light and Snell's Law

Problems and solutions on Refraction of Light

Normal Shift and Lateral Shift due to Refraction of Light

Problems on normal shift Refraction of Light

Universal Gravitational Constant

It is the proportionality constant of Newton's law of gravitation. It is constant over the entire universe and hence gravitational force is independent of location.

The value of the gravitational constant G entering the Universal law of gravitation can be determined experimentally and this was first done by English scientist Henry Cavendish in 1798. The apparatus used by him is schematically shown in figure.

Explanation : The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire.

Two large lead spheres are brought close to the small ones but on opposite sides as shown. The big spheres attract the nearby small ones by equal and opposite force as shown. There is no net force on the bar but only a torque which is clearly equal to F times the length of the bar,where F is the force of attraction between a big sphere and its neighboring small sphere. Due to this torque, the suspended wire gets twisted till such time as the restoring torque of the wire equals
the gravitational torque .

If θ is the angle of twist of the suspended wire, the restoring torque is proportional to θ, equal to τθ. Where τ is the restoring couple per unit angle of twist. τ can be measured independently e.g. by applying a known torque and measuring the angle of twist.

The gravitational force between the spherical balls is the same as if their masses are concentrated at their centers. Thus if d is the separation between the centers of the big and its neighboring small ball, M and m their masses, the gravitational force between the big sphere and its neighboring small ball is.(8.4)

Critical Angle and Total Internal Reflection

Applications of Total Internal Reflection

Problems and Solutions on Critical angle and Total internal Reflection

Refraction of Light Through Curved Surfaces

Power and Focal Length of a Lens

Refraction of Light Through Prism

Problems and Solutions on Refraction of Light Through Prism

Kepler laws of Gravitation

Law of orbits : All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse (Fig.1). This law was a deviation from the Copernican model which allowed only circular orbits. The ellipse, of which the circle is a special case, is a closed curve which can be drawn very simply as follows.

Select two points F1 and F2. Take a length of a string and fix its ends at F1 and F2 by pins. With the tip of a pencil stretch the string taut and then draw a curve by moving the pencil keeping the string taut throughout.(2).

The closed curve you get is called an ellipse. Clearly for any point T on the ellipse, the sum of the distances from F1 and F2 is a constant. F1, F2 are called the focii. Join the points F1 and F2 and extend the line to intersect the ellipse at points P and A as shown in Fig. (2). The midpoint of the line PA is the centre of the ellipse O and the length PO = AO is called the semimajor axis of the ellipse. For a circle, the two focii merge into one and the semi-major axis becomes the radius of the circle.

Law of areas : The line that joins any planet to the sun sweeps equal areas in equal intervals of time (Fig). This law comes from the observations that planets appear to move slower when they are farther from the sun than when they are nearer.