The shape obtained by joining the bases of two solid cones is called a double cone.
Leave this on the lower side of the inclined non-parallel rails. It appears to climb up and reach the higher end. That would mean that it is simply gaining both Kinetic and potential energies without the expense of energy in any other form. That means, it seems violate the law of conservation of energy.
But actually, it is not doing so. When we talk of some object moving up or rolling down, we are thinking of the object as a point mass. And that point is where the whole mass of the object is imagined to be concentrated. The point is called centre of mass. If we observe the height of the centre of mass from the ground /table at the initial and final positions of the double cone, we can make out that it is actually rolling down and not climbing up.
Three plane mirrors are placed mutually perpendicular to each other. Owing to this arrangement, the ray of light incident on any of the mirror undergoes 2 or more reflections and the emergent ray is anti parallel to the incident ray. Being such a simple model, it has a very profound application.
Neil Armstrong when landed on Moon had left the miniatures of this model on the moon. Using them we can find out the distance between Earth and Moon so accurately that we can even make out that Moon is moving away from Earth at the rate of 3cm per year.
(3 cm is a very small distance compared to 3,84,000 km, the average distance between Earth and Moon).
This is achieved by sending a strong LASER beam from Earth and measuring the time take for the beam to reach back the Earth.
Half of this time multiplied by the speed of light in air or vaccum would give the Earth-Moon distance.
Different pictures of a running horse in a sequence are pasted on to the back side of a rotatable plate placed in front of a mirror.
Rotate the plate and view through the slits in it. In the image seen in the mirror, it appears as if the horse is running.
The slits in plate, creates a separation between the images and also allows us to see them in the mirror. When two images are formed on our retina within a very short interval ~1/15th of a second, our brain cannot distinguish them as two separate images.Thi sis known as persistence of vision. This is what gives us the perception of running of the horse.
Three different liquids are filled into transparent tubes of same dimension. A steel ball of same size has been put into each of the tubes. The tubes are sealed at ends and are placed parallel to each other in a frame that can be rotated about a horizontal axis. The metal ball settles at the bottom in each tube. Bring them to top by rotating the frame by 1800. Notice that they all take different time to travel the same distance in the liquids.
Liquids have a property called as viscosity which is a measure of opposition for the free flow of the liquid layers.
The same property is the cause for the difference in time taken by the steel balls in the liquids to reach the bottom.
The Nipkow Disc can be used to illustrate concepts related to sight and vision.
As you see in the photograph, it consists of a disc with holes made along a spiral path. Behind the disc is another disc of the same diameter. A narrow window is cut out along the radius of the second disc. A picture drawn on a transparent sheet is pasted on the window and is illuminated from behind. If we try to look at the picture through the holes, we see a small portion of the picture through each hole. Suppose we now rotate the disc with the holes, we see the entire picture without any discontinuity!
Explanation : The rotating disc allows the holes to scan the entire picture. Depending on the speed of rotation, the rate of scanning also varies. Consequently, the brain retains the pictorial information when the scanning rate is high by virtue of persistence of vision.
Learning Concepts : Persistence of vision, scanning by a TV camera
When not rotating
This model demonstrates the central bulge that all planets have. The extent of bulge is not the same though. We can demonstrate the cause for the bulge as well as the extent of the bulge using this model.
The model comprises a thin metal sheet bent into a circular shape and mounted on to a shaft that can be rotated. When the sheet is not rotated, the circular shape is retained. That’s is to say the radius along the horizontal and the vertical is the same as shown in the photograph on the left. Suppose we rotate the shaft. Then, we notice that a central bulge perpendicular to the axis of rotation. So, the bulge is due to rotation. This is also the reason behind the earth's equatorial bulge. Now, what causes the difference in the extent of bulge? It is the speed of rotation - greater the speed of rotation, more the equatorial bulge.
It is no surprise that Jupiter, the fastest rotating planet in our solar system, shows the greatest bulge.
Learning Concepts : Equatorial Bulge, effect of rotation on the shape of a planet.
In this exhibit we have two points connected by two paths – one that is straight and the other a curved one. When we allow the masses to slide down simultaneously along these two paths, which of the two reaches the bottom end first? Surprisingly, it is not along the straight path! The curved path followed here is a cycloidal path. Newton showed that of all the paths connecting two points, motion along the cycloidal path would take the least time provided the motion is aided by gravity alone.
By connecting different points in plane with straight lines according to a specific rule one can finally bring about the appearance of some beautiful curves like cardioids, nephroid, etc., These are all called curve envelopes. To bring about the appearance of a cardioid, here are a few steps: Construct a circle and mark points on it at every 10 degree. Number them from 0 to 35. Connect the point numbered n to 2n. If 2n > 36, connect n to the remainder of (2n/36) . At the end you can notice the appearance of the heart shaped curve – Cardioid. You can also try connecting n to 3n, 4n, 5n, etc in a similar way or even increase the number of points on the circle and check out what happens.
Here is a trick to guess any number between 1 and 31. Prepare five cards as shown below: Ask your friend to keep in mind any number between 1 and 31. Show the five cards and ask to select the cards containing their secret number . To guess the secret number, all you have to do is to add the top most numbers of the selected cards.
Cycloid is the locus of the path traced by a point on the circumference of a circular disc as the disc rolls on a straight line without slipping. To trace this curve, we have the following model:- A circular disc bearing a hole close to its circumference is placed on an alluminium channel fixed to a board. A sketch pen is inserted into the hole. As the disc rolls, the sketch pen traces the curve - "Cycloid"
Cardboard, pencil, scale and scissors Procedure: Take a square ABCD of side 'a'. Draw a small square BEFG of side 'b' and cut it out. The area of remaining part is a2 - b2 . Cut along FD and arrange the two parts to get a rectangle as shown in figure (2) The sides of this rectangle will be
(a+b) and (a-b)
a2-b2 =(a+b) (a-b)
Materials Required: Steel spheres of about 2 mm diameter, a neodymium magnet of about 10 mm in diameter, a non-magnetic U-channel or a transparent plastic pipe
Procedure : Place the magnet at a small distance from one of the channel / pipe. Attach two or three steel spheres to the magnet as shown in the figure Gently roll the ball that is free, towards the magnet. As soon as this ball strikes the magnet, the ball that is placed farthest from the magnet shoots off at very high speed.
Reason : The steel ball, even if it starts with a small velocity, undergoes rapid change in its speed as it approaches the magnet. The speed of the ball just before colliding with the magnet will be large compared to what it started with. The collision transfers the momentum to the magnet which, in turn, passes it on to the steel balls. The farthest one being attracted only weakly, launches off at high speed.
Apparatus Required: Sun control film, cardboard, gum.
Cut a rectangular strip of sun control film and paste it on a cardboard of same size such that there are no wrinkles and allow it to dry.
Bend it such that it is a part of a cylinder and you see your own inverted image.
Rotate the same bent strip by 900 and surprisingly the image also rotates but by 1800 and you can see an erect image.
This happens because; the strip forms a part of cylindrical mirror. The curvatures along the longer and the shorter sides are different and so are the focal lengths. Hence the image formation for a given object distance is different.
A person standing in front of a plane mirror can see his image in the mirror.
If two mirrors are hinged together and are kept 1800 apart, even then there will be a single image. If the angle between the mirrors is reduced, we begin to see another image forming and there will be 'two' complete images when the angle between the mirrors becomes 1200.
As we further reduce the angle to 900, we will have 'three' complete images. Likewise, we will have 'four' images when the angle is 720, five images at 600 and so on. As the angle between the mirrors is reduced further, the number of images would increase and it can be generalised as follows :-
This is known as multiple reflection where the image of the object itself serves as the object for further images.
Suppose the angle between the mirrors is made 00, then as per the formula there should be infinite number of images. But practically it is not so. This is because of the absorption loss that happens at every reflection. As a result we see many images lined up one behind the other but because of the absorption losses, the images get blurred after a certain reflections and we cannot see beyond that.
In this set up we have parallel inclined rails as shown in the figure. A cylinder placed at the top rolls down very quickly. Whereas, a wheel-and-axle weighing same as the cylinder rolls down very slowly.
Reason : The cylinder as well as the wheel-and-axle move down under the influence of gravity. Both, however, do not move down at the same speed, even though their potential energies are the same at the top of the railing.
In this experiment, both objects possess kinetic energy of translation and kinetic energy of rotation. The potential energy they possess is divided between the two forms of kinetic energy. The total mechanical energy, ie the sum of potential energy, rotational energy and translational energy is conserved. And, the sum is same for both the objects. However,what fraction of the potential energy manifests as translational kinetic energy is dependent on the distribution of mass in a given object. On account of this, much of the kinetic energy for the wheel-and-axle goes into rotation. Consequently, the forward motion is slow. For a cylinder, the mass distribution is such that a comparatively lesser fraction of the kinetic energy goes into rotation. Hence, a cylinder reaches the bottom of the railing faster than the wheel-and-axle.
Learning Concepts : Conversion of potential energy into kinetic energy, translational kinetic energy, rotational kinetic energy, conservation of energy, motion under gravity, moment of inertia - inertia of rotation.
This is a classic experiment first demonstrated by the well-known scientist John Tyndall to demonstrate the total internal reflection of light. The apparatus is a tall glass cylinder with a spout near the bottom. The spout is closed and the cylinder is filled up with water. The spout can be illuminated from the back with the help of a LASER pointer. On opening the spout, LASER light bends all along the trajectory of water.
Reason : This is due to total internal reflection. If light is incident in the denser medium at an angle greater than or equal to the critical angle, light undergoes total internal reflection.
Learning Concepts : refraction of light, Total Internal Reflection
This is an electric panel board comprising three bulbs connected in series. Input voltage and current as well as voltage across each bulb can be measured with the voltmeters and ammeter provided.
We know that the current passing through each of the bulbs for this configuration is the same. Therefore, the voltage across each of the bulbs will be proportional to the resistance of the glowing bulb. The sum of the voltage drop across the three bulbs will be equal to the input voltage.
You can select bulbs of same wattage or different ones. Check the voltage drop across each bulb in each case.
Learning Concepts : dependence of voltage drop on the resistance, Ohm's law, conservation of energy, conversion of one form of energy into another.
A wave is a disturbance from an equilibrium condition that travels or propagates from one region of space to another. Our understanding of everything around us, in one way or the other, depends on studying waves of different kinds. The model here illustrates the propagation of one kind of waves known as transverse waves
Example : Electromagnetic waves
Two vertical supports have strings, spaced about 10 cm, between them as shown in the photograph. Aluminium rods measuring about one foot in length are fixed perpendicular to the strings and one centimetre apart.
Gently pull down a rod at one of the ends and release it. Subsequently, all the rods along the string execute an up-down motion while the disturbance itself travels in a direction perpendicular to that motion. This is how transverse waves propagate.
Further exploration : Try to set up a standing wave by continuously moving one of the Aluminium rods up and down at a uniform speed.
The pupil in the eye is an opening through which light reaches the retina and the images we see are formed. The dimension of the pupil is altered by certain muscles in the eye in accordance with the intensity of the surrounding light. The size is maximum in darkness and minimum under intense light – say, during a hot summer afternoon.
The change in the dimension of the pupil can be easily seen in this exhibit.,
Look at the pupil in the concave mirror. As you continue to gaze, press and hold the Bell switch provided. As light from the bulb falls on your eyes, you will see the pupil constricting. It gradually expands to its earlier size once the light is switched off.
The ability of the pupil to alter its size is important if one were not to go blind.
Persistence of Vision
Here, we have a shaft to which irregularly shaped thick wires are attached. It does not seem to resemble any familiar object. Once the shaft is set into rotation, we perceive a lotus out of the seemingly irregularly positioned wires.
Learning Concepts : Persistence of Vision; perception