### what is the relationship between mass and momentum? | Yahoo Answers

E.g. An object has mass 2kg and velocity 4m/s. (The negative sign means the direction of velocity is negative, i.e. opposite to the initial. This is not the case. Both will reach the ground at the same time. v2 = u2 + 2gs. ( independent of mass) s= 1/2 at2 (independent of mass). Short Answer. 7 Center of Mass and Momentum. .. problems an equation, or a number (or set of equations or numbers). It is a.

As a prelude to reading my answer, you should read an earlier answer and the earlier answers referred to in that answer. The graph here shows the results derived or cited in that earlier answer. The three graphs all show what is observed of your motion as seen by the twin on earth.

Now, since I have set this up as seen from earth, let me specify the time you travel as the time of your trip out as observed from earth: Light would take 2.

We can get a rough estimate of your clock reading by approximating your average relative speed as 0. What happend to accelaration due to gravity if the earth stops rotating? Because of the centrifugal force, g appears to be somewhat smaller than it really is, but the amount is very tiny.

This effect depends on your latitude and is zero at the poles and greatest at the equator. Also because of this effect, the acceleration is not directly toward the center of the earth except at the poles and equator. Hello, is the mass of a person on a spaceship to provide a suitable upward force important in designing a spaceship? My teacher says otherwise but upon researching I found out that additional fuel is required for every kg of payload that will be sent out into space.

If the ship and all the fuel are much bigger than the mass of the person, then you could neglect the mass of the person in any calculations you know; in other words, the rocket launch would be, as close as you could hope to be measure, identical whether or not an astronaut was on board.

## Questions & Answers

However you are also right that the amount of fuel you need depends on the payload you want to deliver, and that would include everything which is not fuel. You might find the an earlier answer illuminating. How exactly do electrons in electric discharges generate radio waves? Whenever someone uses an AM radio while there are electric sparks like lightning strikes nearby the radio waves they emit can be detected.

Any time an electric charge is accelerated it emits electromagnetic radiation. There are many electrons in the spark which accelerate under the influence of the electric fields they experience. I just read about the kilogram being defined by measuring the current of an elector-magnet to balance a scale. How can various electromagnets have exactly the same force to current ratio?

Would variations in the purity of the conductor, variations in the exact coil shape, etc. What am I missing about this new designation?

You cannot use any old electromagnet. There is an exquisitely accurate balance called the Kibble balance which is used. Is the following statement correct? Net radiated energy is made up of emitted and absorbed energy.

I stated that it was incorrect based on the fact that "made up of" usually means putting two or more things together aka addition. Net radiated energy is the difference between emitted energy and absorbed energy. What is the correct answer in this case and why? I do not believe that there is a hard and fast definition of what "net radiated energy" is. It is a matter of semantics. However, radiated energy usually means energy emitted and absorbed energy means energy absorbed; therefore, I would say that this is an incorrect statement because net radiated energy would mean the sum of all radiated energy, absorbed energy having nothing to do with it.

Your reason is quite shaky because "made up of" is even more semantically ambiguous than "net radiated"; it would simply imply that "net" means total energy flux. How is momentum conserved for single or double slit diffraction? I have a photon gun that I can dial the intensity down to fire one photon at a time.

The photon then passes thru two closely spaced slits double slit experiment instead of appearing on the screen directly behind the slits, the photon ends up to the side after many, many photons the interference pattern appears however, for the single event of a single photon, how is momentum conserved? Since the photon ended up to the side, it was no longer travelling in the purely X direction, therefore shouldn't the photon have exchange d momentum with the slit somehow?

If the interference pattern remains, then how do we account for the photons change in momentum? This is for a single event, one photon, not expectation value of many, many photons. You are forgetting that the photon goes through both slits, is being forced if you like to assume its wave-like identity.

It behaves like a wave until something makes it act like a particle, so it is a wave spreading out in both directions, so its net momentum in the direction parallel to the screen is zero.

When the screen is encountered it is a "measurement" which collapses the wave function at some point.

I can imagine 2 similar objects rotating around a sphere at the same velocity but at different orbits. One object would rotate around the sphere faster than the other, right? What is puzzling to me is that if I think of both objects going now in a straight line one could not say that one object was going faster than the other.

Can someone help me through this? Is there a subtlety here? You want to say same speed, not same velocity, but I get the idea. Say one orbit is twice the radius as the other. Then the smaller orbit has a circumference half that of the larger.

So each time the object in the larger orbit goes around once, the one in the smaller orbit goes around twice. But they still have the same speed. The successful candidates should be extremely dynamical and analytically minded individuals.

H That statement on inviolable patterns was very beautiful, very true. Also probably why it was so difficult to formulate in the language of linear equations and operators. Sure, we may be satisfied that natural law dictates certain phenomenological constructs, but not because what we find is satisfactory! At least with the tools we currently have. This goes back to that spat you guys had with Paul Davies.

### what is the relation between momentum and velocity? | Yahoo Answers

This is all assuming there is no real problem with the models as they stand today, and that people are at a stage of fundamental knowledge where they are reduced to existential questions, and everything else is fine. But I feel that we are going to get a much better perspective on things soon, and for that I will be very thankful. Sam Cox Very well done, Sean! Perhaps you could also point to the connection between the conservation of momentum and invariance of the laws of physics under translations of the coordinates.

That connection between a symmetry and a conservation law has always amazed me. Finally I think that you have some enough deep thoughts in order to try to build a philosophy, so good luck if you want to go in this way ; before to build mine I was from the group of the ones who did not want to accept the notion of God, but even with all the bad bias I had, the logic I needed was the strongest.

Ernst Zermelo was one of the major advocates of such a view, and he was also responsible for the development of much of axiomatic set theory. As an alternative to set theory, others have argued for category theory as a foundation for certain aspects of mathematics. The intuitive approach silently assumes that all objects in the universe of discourse satisfying any defining condition form a set.

Axiomatic set theory was originally devised to rid set theory of such antinomies[3]. The most widely studied systems of axiomatic set theory imply that all sets form a cumulative hierarchy. Such systems come in two flavors, those whose ontology consists of: This includes the most common axiomatic set theory, Zermelo—Fraenkel set theory ZFCwhich includes the axiom of choice. Fragments of ZFC include: They state that any effectively generated formal theory in which all arithmetic truths can be proved is inconsistent; hence, any such consistent formal theory that can prove some arithmetic truths cannot prove all arithmetic truths.

The theorems are of considerable importance to the philosophy of mathematics. One of the simplest examples of a category which is a very important concept in topology is that of groupoid, defined as a category whose arrows or morphisms are all invertible.

Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.

Category theory provides both with a unifying notion and terminology. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in —45, in connection with algebraic topology. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism.

In many situations this is too much to hope for and it is more prudent to aim for a more modest goal, classification up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, the converse, using topology to solve algebraic problems, is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. They appear in virtually every branch of modern mathematics and are a central unifying notion.

The branch of mathematics that studies topological spaces in their own right is called topology. The elements of X are usually called points, though they can be any mathematical objects. A topological space in which the points are functions is called a function space.

A set may be neither closed nor open, either closed or open, or both. A set that is both closed and open is called a clopen set. In older operating systems with cooperative multitasking, infinite loops normally caused the entire system to become unresponsive.

With the now-prevalent preemptive multitasking model, infinite loops usually cause the program to consume all available processor time, but can usually be terminated by the user. Thus, the angular velocity will be different. It started from rest from the first station and comes to rest at the second. Let total distance be x. Substitute for the values of time from above and the highest velocity attained is v and then take the ratio.

Give examples to demonstrate Newton's Laws of Motion. Place a piece of cardboard on it. On top of the cardboard place a coin. Now flick the cardboard away with your finger. The coin will not follow the cardboard but drop into the tumbler. This is because there is no force acting on the coin and it continues to stay in a state of rest.

A cricketer moves his hands back when taking a catch.

This to increase the time period over which the velocity of the ball reduces from a high value to zero. Or in other words the acceleration is reduced. Thus the force transferred to the cricketer's hand is reduced. When a rocket is launched, the downward action of the exhausted gases results in the upward reaction on the rocket, causing it to rise.

How do you solve two dimensional trajectory problems? Trajectory problems may be put into two categories. Horizontal projection and angular projection. During its motion the object covers horizontal distance due to horizontal velocity and vertical distance due to vertical velocity. So each problem can be simplified into two one dimensional problems by taking the components of position, velocity and acceleration along the horizontal and vertical directions. Let us consider the case of horizontal projection.

The object is projected with initial horizontal velocity u. Since the velocity of the object in the horizontal direction is constant so the acceleration ax along horizontal direction is zero. If the initial position of the object was x0, y0 the position of the object at any time t along the horizontal direction i.

If we put the origin of the co-ordinate system at the initial position then the co-ordinates of the initial position become 0,0. Let us take the downward direction as positive. Thus the acceleration in the vertical direction is g 9. This is the equation of a parabola, which is symmetric about the y-axis. Hence the path of the projectile projected horizontally from a certain height from the ground is a parabolic path. How fast must a roller coaster travel around a vertical circular track with radius 10m if it is not to fall from the track?

How long would it take for a ball to fall from a 70 feet tower? This is a problem of free fall. Here, h is the height by which the body falls, u is the initial velocity, t is the time taken to fall by a distance h and g is the acceleration due to gravity. By substituting we can get the answer. If you fire a bullet from a level gun and drop a bullet at the same time, both the bullets will hit the ground at the same time.

Both the bullets have the same acceleration in the vertical direction which is the acceleration due to gravity. Also both the bullets have zero initial velocity in the vertical direction. The bullet fired from the gun has an initial velocity in the horizontal direction but it will not affect the motion in the vertical direction.

Since, both the bullets have to cover the same vertical distance, they will take the same time to do to it and will hit the ground at the same time. What is the minimum speed the pilot of an aircraft should have so as to successfully loop a vertical loop without falling at the top of the loop? Also what is the thrust acting on the aircraft?

The forces acting on the aircraft are - the weight mg acting downwards and the force F by the air upward.

### Momentum and Kinetic Energy? | Yahoo Answers

This is the minimum value of velocity at the highest point. If we substitute the value for v', we get, v? Thus, for looping the loop the minimum speed the aircraft should have at the lowest point should be?

Also the maximum thrust on the aircraft will be at the lowest point. When a ball is moving on a smooth plane, it will have acceleration only when there is an external force. Can it be said that the above statement is wrong because when ball is on a smooth inclined plane, it still has acceleration? To understand this question, let us first understand Newton's first law. It says that if the vector sum of all the forces acting on a body is zero then and only then the body remains unaccelerated i.

Let us consider a body moving on a smooth horizontal surface with a uniform velocity. The forces on the body are the gravitational force exerted by the earth and the contact force or the normal reaction exerted by the plane surface on the body.

These forces are equal and opposite and they cancel out. Thus the net force acting on the body is zero and the body remains unaccelerated. Now, let us consider the body moving on a smooth inclined surface.

Thus the body will have acceleration. The prism should be placed in such a manner that if we view the prism from the top, we see one of the triangular faces of the prism. Then one angle of the prism can be taken as the refracting angle. Thus the refracting edge will become vertical. The incident ray falls on one of the faces which contains one of the sides making the refracting angle.

The refracted ray emerges from the face containing the other edge of the refracting angle. Determine the size and location of the mouse's image. Describe the mouse's image in the mirror. Where is its image? The image of an oncoming car is at 3.

What is the actual position of the car? How large and at what distance from the lens will the ant appear to be? Describe the image of the mouse as seen through the lens.

## Relationship between mass and velocity?

The focal length of the lens is At what distance is the screen from the lens? How large will a figure 2. We have to know the lens and the mirror formulae and the sign convention to solve the above problems. Sign convention is that all distances measured in the same direction as the incident light are taken as positive and in the opposite direction are taken as negative.

In case of mirrors, distances are measured from the pole and in case of lenses, the distances are measured from the optical center. Thus, the focal length of a concave mirror will be negative and that of a convex mirror will be positive. Also, the focal length of a convex lens will be positive and that of a concave lens will be negative.

Thus the image is real and inverted and at a distance of 30cm from the mirror and on the same side as the object. Thus, image is on the same side as the object at a distance of 36cm from the mirror. Substitute in the mirror formula to find u. Thus, the size of the image of an object of size 2.

For a real image u is negative and v is positive. A block of glass has a critical angle of 39 deg. What is the index of refraction of the glass? Also, i is the angle of incidence and r is the angle of refraction. In the problem, light is passing from the medium glass to the medium air at the angle of incidence being equal to the critical angle. In such a case, the angle of refraction is equal to 90 deg.

For a convex lens, R1 is positive and R2 is negative. For a concave lens, R1 is negative and R2 is positive. When the transmission axes of two Polaroid films are perpendicular to each other, what is the percentage of incident light which will pass the two films? When incident light falls on the first Polaroid film, it allows only those vibrations to pass through which are parallel to its own transmission axis.

The emerging light has vibrations confined to one plane only which is perpendicular to the transmission axis of the second Polaroid film. Thus no light will pass through the second Polaroid film. Why would it be impossible to obtain interference fringes in a double slit experiment if the separation of the slits is less than the wavelength of light used?

The above diagram shows the double slit experiment. Thus it is impossible to obtain interference fringes in a double slit experiment if the separation of the slits is less than the wavelength of the light used.

Moreover, if d is less than wthen S and S' stop being two coherent sources but rather behave like a single source. A noisy machine in a factory produces a decibel rating of 65dB. How many identical machines could you add to the factory without exceeding the dB limit? Let the intensity of sound produced by one machine be I.

Let I' be the intensity of sound when x number of machines are used to produce decibel rating of 95dB. This means that more machines can be used. Explain the terms the fundamental mode of vibration and resonant air columns. Organ pipes are musical instruments which are used for producing musical sounds by blowing air into the pipe. Longitudinal stationary waves are formed on account of superimposition of incident and deflected longitudinal waves.

The fundamental mode of vibration is a simplest mode of vibration and the frequency produced in this mode is the lowest frequency that can be produced and is called the fundamental frequency that can be produced.

For example in a closed organ pipe closed at one end in its fundamental mode of vibration the open end acts as an antinode.

This is because the air can move freely there. The closed end acts as a node because air cannot move too and fro there. Resonant air column It is an apparatus which consists of a long cylindrical tube filled with water having its lower end joined by a rubber tubing to a moveable reservoir of water. The cylindrical water tube is fixed along a meter rod and the level of water in it can be lowered or raised with the help of a reservoir.

A tuning fork of known frequency is gently struck against a rubber pad and is held horizontally at the mouth of the water tube. At the same time the level of water in the tube is lowered till a loud sound is heard.