Transverse and longitudinal waves

Transverse and longitudinal waves :

On the left side of Figure 1 , a pulse travels on a string. As the pulse passes point P on the string, the point moves up and then back to the equilibrium position. Each segment of the rope moves only perpendicular to the motion of the wave. This type of traveling wave is called a transverse wave.

Figure 1

Transverse (a) and longitudinal (b) waves.

The right side of Figure 1 shows the pulse propagated along a stretched spring. In this case, the individual points along the medium (the spring) travel back and forth parallel to the motion of the pulse. This type of traveling wave is called a longitudinal wave. Sound waves are longitudinal waves.
I hope the above explanation was helpful.

Summary to Reflection of Light

In this lesson .. let me try to help you on reflection of light.

Introduction -

It is a matter of common experience that the objects inside a dark room, which are invisible, become visible when the room is illuminated by a source of light. Thus light can be defined as the external cause responsible for the sensation of vision.

When a ray of light falls on any surface, a part of the light is sent back to the same medium. This phenomenon where the incident light falling on a surface is sent back to the same medium is known as reflection.

There are two types of reflection of light:

• Regular reflection

• Irregular reflection

Regular reflection -

Regular Reflection on a Smooth Surface

Regular reflection takes place when a ray of light is incident on a polished smooth surface like a mirror. Here the reflected ray of light moves only in a fixed direction.

Irregular reflection-

Irregular reflection or diffused reflection takes place when a ray of light is incident on a wall or wood, which is not smooth or polished. In this case, the different portions of the surface reflect the incident light in different directions. In such cases no definite image is formed, but the surface becomes visible. It is commonly known as scattering of light. Thus diffused reflection makes non-luminous objects visible.

Not all light, which hits an object, is reflected. Some of the incident light is absorbed. The brightness of an object depends on the intensity of the incident light and also on the reflectivity of the object.

If a surface allows the entire incident light to undergo regular reflection then it will become invisible.

I hope my information on this topic is more helpful to you .. Keep reading and leave your comments..

Explain Centripetal acceleration

Let us study about centripetal acceleration,

Property of the motion of an object traveling in a circular path. Centripetal describes the force on the object, directed toward the centre of the circle, which causes a constant change in the object's direction and thus its acceleration. The magnitude of centripetal acceleration a is equal to the square of the object's velocity v along the curved path divided by the object's distance r from the centre of the circle, or a = v2/r.

The radial component of the acceleration of a particle or object moving around a circle, which can be shown to be directed toward the center of the circle. Also known as radial acceleration.

The gravitational acceleration at earth's surface is 9.8 m/s/s. The centripetal acceleration on earth's surface at
the equator is 0.006 m/s/s. At earth's equator the gravitational force and the centripetal force are both in the same vertical direction. However, at other places on earth's surface the centripetal force is at an angle equal to a place's latitude, and the centripetal force is reduced due to reduced distance to the axis of earth's rotation. One would deduce that at these places there's a horizontal component of centripetal force, that would cause a person to lean slightly toward earth's pole to maintain his or her balance.
Hope the above explanation was helpful.

Elasticity of solids

Let us study about elasticity of solids,
Elasticity is the ability of a solid to return to its initial shape after having an outside force applied to it and then removed. An object with a high level of elasticity is able to have its shape changed a great deal, while still being able to return to its original form. Solids with little or no elasticity either become permanently deformed or break when a force is applied to them. The term elasticity can also be used to describe the ability of processes or systems to stretch or be flexible.

Due to the molecular make up of solids, liquids, and gases, they all react differently to outside stresses. The molecules that make up a solid are very close together and are found in a precise arrangement. This means that there is little room for give when a force is applied to a solid. The molecules of liquids and gases are spread further apart, and move more freely than those of solids. When a force is applied to liquids and gases, they can either flow away from or around the force, or be compressed a great deal, unlike most solids.

There are three different classes of force, or stresses, that can affect solid objects. The first is tension, also called stretching, which occurs when equal but opposite forces are applied to either end of the object. Compression is the second type of stress, which occurs when an object is put under pressure, or the force pushing on the solid is at 90 degrees to its surface. Imagine crushing an empty paper towel roll between your hands with your hands at either end. The final type of stress is shear, which happens when the force is parallel to the surface of the object.
Hope the above explanation helped you, now let us study about states of matter.

Center of Mass

Let us learn about center of mass,

Every object has a center of mass, which can be thought of as the point that is as close as possible to every piece of an object. Usually the center of mass is found within the object. For example, the center of mass of a ball is the very middle of the ball, and the center of mass of a book is the middle of the book. Where do you think the center of mass of your pencil is? How about the center of mass of your body? Talk about this with you mentor.

The center of mass determines whether or not something will fall over. Imagine pushing over a refrigerator. At the beginning, the center of mass is directly over where the fridge touches the ground.

If you push the refrigerator a little, it will fall back into place. If, however, you push it enough so that the center of mass is past the piece of the fridge that is touching the ground, it will fall.
Hope the above explanation helped you, now let us study about Force.

Hydraulic Machines

Let us learn about Hydraulic Machines,
Let us now consider what happens when we change the pressure on a fluid contained in a
vessel. Consider a horizontal cylinder with a piston and three vertical tubes at different
points. The pressure in the horizontal cylinder is indicated by the height of liquid column in
the vertical tubes.It is necessarily the same in all. If we push the piston, the fluid level rises in
all the tubes, again reaching the same level in each one of them.
This indicates that when the pressure on the cylinder was increased, it was distributed
uniformly throughout. We can say whenever external pressure is applied on any part of a
fluid contained in a vessel, it is transmitted undiminished and equally in all directions.
This is the Pascal’s law for transmission of fluid pressure and has many applications in
daily life.

A number of devices such as hydraulic lift and hydraulic brakes are based on the Pascal’s
law. In these devices fluids are used for transmitting pressure. In a hydraulic lift as
shown in Fig. two pistons are separated by the space filled with a liquid.
Schematic diagram illustrating the principle behind the hydraulic lift, a device used to lift heavy loads.

A piston of smallcross section A1 is used to exert a force F1 directly on the liquid. The pressure P = F1/A1 is
transmitted throughout the liquid to the larger cylinder attached with a larger piston of area A2,
which results in an upward force of P × A2. Therefore, the piston is capable of supporting a
large force (large weight of, say a car, or a truck, placed on the platform) F2 = PA2 = F1A2 / A1 . By changing the force at A1, the platform can be moved up or down. Thus, the applied force has
been increased by a factor of A2/A1 and this factor is the mechanical advantage of the device.
Hope the explanation helped you, now let us learn about Transmission of Pressure in Liquids.

Atmospheric Pressure and Gauge Pressure

Let us learn about Atmospheric pressure,
The pressure of the atmosphere at any point is
equal to the weight of a column of air of unit
cross sectional area extending from that point
to the top of the atmosphere. At sea level it is
1.013 × 105 Pa (1 atm). Italian scientist
Evangelista Torricelli (1608-1647) devised for
the first time, a method for measuring
atmospheric pressure. A long glass tube closed
at one end and filled with mercury is inverted
into a trough of mercury as shown in Fig.
This device is known as mercury barometer. The
space above the mercury column in the tube
contains only mercury vapour whose pressure
P is so small that it may be neglected. The
pressure inside the column at point A must
equal the pressure at point B, which is at the
same level. Pressure at B = atmospheric
pressure = Pa
Pa = ρgh
where ρ is the density of mercury and h is the height of the mercury column in the tube.
In the experiment it is found that the mercury column in the barometer has a height of about
76 cm at sea level equivalent to one atmosphere (1 atm). This can also be obtained using the
value of ρ in Eq. A common way of stating pressure is in terms of cm or mm of mercury
(Hg). A pressure equivalent of 1 mm is called a torr (after Torricelli).
1 torr = 133 Pa.
The mm of Hg and torr are used in medicine and physiology. In meteorology, a common unit
is the bar and millibar.
1 bar = 105 Pa
Now, let us learn Measurement of Atmospheric Pressure.

Variation of Pressure with Depth

Let us learn about Variation of Pressure with Depth.
Consider a fluid at rest in a container. In Fig. point 1 is at height h above a point 2.
The pressures at points 1 and 2 are P1 and P2 respectively. Consider a cylindrical element of
fluid having area of base A and height h. As the fluid is at rest the resultant horizontal forces
should be zero and the resultant vertical forces should balance the weight of the element. The
forces acting in the vertical direction are due to the fluid pressure at the top (P1A) acting
downward, at the bottom (P2A) acting upward. If mg is weight of the fluid in the cylinder we
have (P2 − P1) A = mg
Now, if ρ is the mass density of the fluid, we have the mass of fluid to be m = ρV= ρhA so
that
P2 − P1= ρgh
Fluid under gravity. The effect of gravity is illustrated through pressure on a vertical
cylindrical column.

Pressure difference depends on the vertical distance h between the points (1 and 2), mass
density of the fluid ρ and acceleration due to gravity g. If the point 1 under discussion is
shifted to the top of the fluid (say water), which is open to the atmosphere, P1 may be replaced
by atmospheric pressure (Pa) and we replace P2 by P. Then Eq. gives
P = Pa + ρgh
Thus, the pressure P, at depth below the surface of a liquid open to the atmosphere is
greater than atmospheric pressure by an amount ρgh. The excess of pressure, P − Pa, at
depth h is called a gauge pressure at that point.
Hope the above explains about Variation of Pressure with Depth, now let me explain about Vapour pressure.

Pascal’s Law

Let me give you some introduction on pascal's law

The French scientist Blaise Pascal observed that the pressure in a fluid at rest is the same at all points if they are at the same height. This fact may be demonstrated in a simple way.
Fig : Proof of Pascal’s law. ABC-DEF is an element of the interior of a fluid at rest. This element is in the form of a right angled prism. The element is small so that the effect of gravity can be ignored, but it has been enlarged for the sake of clarity.

Figure shows an element in the interior of a fluid at rest. This element ABC-DEF is in the
form of a right-angled prism. In principle, this prismatic element is very small so that every
part of it can be considered at the same depth from the liquid surface and therefore, the effect
of the gravity is the same at all these points. But for clarity we have enlarged this element.
The forces on this element are those exerted by the rest of the fluid and they must be normal to
the surfaces of the element as discussed above. Thus, the fluid exerts pressures Pa, Pb and Pc on
this element of area corresponding to the normal forces Fa, Fb and Fc as shown in Fig. 10.2 on the faces BEFC, ADFC and ADEB denoted by Aa, Ab and Ac respectively. Then Fb sinθ = Fc, Fb cosθ = Fa (by equilibrium)Ab sinθ = Ac, Ab cosθ = Aa (by geometry)
Thus,Hence, pressure exerted is same in all directions in a fluid at rest. It again reminds us that like other types of stress, pressure is not a vector quantity. No direction can be assigned
to it. The force against any area within (or bounding) a fluid at rest and under pressure is
normal to the area, regardless of the orientation of the area.

Pressure

Let me explain what is pressure,
Imagine when a sharp needle when pressed against our skin pierces it. Our skin, however, remains intact when a blunt object with a wider contact area (say the back of a spoon) is pressed against it with the same force. If an elephant were to step on a man’s chest, his ribs would crack. A circus performer across chest chest a large, light but strong wooden plank is placed first, is saved from this accident. Such everyday experiences convince us that both the force and its coverage area are important. Smaller the area on which the force acts, greater is the impact. This concept is known as pressure.

When an object is submerged in a fluid at rest, the fluid exerts a force on its surface. This force is always normal to the object’s surface. This is so because if there were a component of force parallel to the surface, the object will also exert a force on the fluid parallel to it; as a consequence of Newton’s third law. This force will cause the fluid to flow parallel to the surface.

Since the fluid is at rest, this cannot happen. Hence, the force exerted by the fluid at rest has
to be perpendicular to the surface in contact with it. This is shown in Figure.
Hope the above example explains you about pressure, now let me give you more examples.