## Introduction

This paper presents energy and momentum as applied in the daily life. It is important first to define energy and momentum separately so as to grasp the technical terms used during the discussion of the topic. Relationship between energy and momentum will be drawn with reference to potential and kinetic energy. The analysis will also note application of both energy and momentum to our daily life.

## Features of energy and momentum as applied in daily life

As defined by many scientists, energy is termed as the ability to do work. Work done is when a force is incurred by a system over a distance. There are several forms of energy in existence. Examples of them are: kinetic energy, electrical energy, potential and heat energy (Llewellyn, 40).

Potential energy is the stored energy in a system. Water in a dam has potential energy while a body which is inclined on a plane and not moving also has potential energy. Kinetic energy is the energy oriented to move. When water in a dam runs down a tunnel it will gain kinetic energy.

The body had been inclined on a plane gains kinetic energy when it starts to move down the plane. According to the law of conservation of energy it states that energy can neither be created nor destroyed but can be transformed from one form to another (Tipler, 23). An example is water in a dam which is used to turn the turbine in the hydro electric power station.

Initially, still water possesses potential energy but on flowing down the tunnel to the turbine, the potential energy changes to kinetic energy and finally turns the turbine and which rotates the current carrying conductor inside a strong magnetic field to generates the electrical energy.

Momentum is the quantity of motion possessed by a moving object. To calculate the momentum of a moving body, we multiply the mass of that body by the speed at that instance. Spontaneity is considered in the calculation. Stationary bodies has zero momentum because they don’t have any motion hence their velocity is zero (Serway, 21).

Taking the picture of a body inclined in a plane, it gains speed on moving down the plane consequently increasing momentum such that the final momentum is higher than the initial momentum. Average momentum is therefore calculated as the initial momentum added to the final momentum and the result is divided by two (Smil, 13). Where two bodies in motion collide, momentum before and after is conserved. As a Vector quantity, momentum has both path as well as scale.

## Relationship between energy and momentum

Considering the case of water in a dam, both potential energy and kinetic energy can be speculated for its effectiveness by the use of system of equations. From the equations, relationship between energy and momentum can be deduced.

Total energy (Et) of the system represents the sum of kinetic energy and potential energy, Et = Ke + Pe…eq (i). From the definition of Energy as ability to do work, we obtain Energy = Force (F) × distance (X) …eq (ii). Considering a small change in the distance given by Δx, Energy = F.Δx…..eq (iii). Displacement formulae states that; displacement = velocity (v) × time (t). Therefore Δx = Δv.t. Replacing this equation in equation iii above we get the following: Energy = F.vΔt……eq (iv). From Momentum (p) = Mass × velocity= Force × velocity (Halliday, 12). Taking a small change in momentum, equation (iv) becomes Energy = Δp⁄Δt.v. Δt = Δp.v =v. Δ (mv) ….eq (v). Taking the dot product of the above equation v. we get Δ(v.v) = (Δv).v + V.( Δv) = 2(v. Δv).

For a constant mass, equation (v) becomes v. Δ (mv) = m/2Δ (v.v) = m/2Δv^{2} = Δ (mv^{2}/2)…………eq (vi)

Therefore Energy = f. Δx = Δ (mv^{2}/2). Taking the integral of both sides from initial to the final i.e. from the time water started moving down the dam through the tunnel we get the kinetic energy of the system. ∫f. Δx = ∫ Δ (mv^{2}/2) = mv^{2}/2

Therefore kinetic energy has been derived. Ke= mv^{2}/2

From eq (i) taking the negligible potential energy we have E t = Ke = mv^{2}/2

Kinetic energy is therefore related to momentum in the above equation.

Momentum and energy is applicable in everyday undertakings, for example when there is a head on collision the policeman inspecting the accident will determine the distance of braking using the inelastic collision of momentum.

To further supplement on the discussion, an example to show relationship between kinetic energy and momentum is when playing pool table game where one has to hit a ball from the angle. The final direction is determined by the head on collision between the two balls and the impact will result in one ball moving in another direction.

## Conclusion

This paper offered a vivid illustration of energy and momentum. It was evident from the discussion that momentum has magnitude and will act in the direction of a force. Whereas energy can be converted from one form to another, momentum cannot be changed from one form to another but can be converted to other forms. In a collision of bodies for a closed system, the momentum of the two colliding bodies can be exchanged. As mentioned in the literature energy is related to momentum in the following equation Et = Ke = mv^{2}/2.

## Works Cited

Halliday, David and Resnick, Robert. *Fundamentals of Physics*. New York: John Wiley & Sons, 2007.

Llewellyn, Ralph and Tipler, Paul. *Modern. Physics.* Boston: W. H. Freeman, 2002.

Serway, Raymond and Jewett, John. *Physics for Scientists and Engineers.* Belmont, CA: Brooks/Cole, 2004.

Smil, Vaclay. *Energy in nature and society: general energetic of complex systems*. Cambridge: Cambridge university press, 2008.

Tipler, Paul. *Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics. Boston:* W. H. Freeman, 2004.