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Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

Discussion

I have touched on collisions in one dimension in earlier modules. I will deal with collisions in a more rigorous manner in this module, and will also extendthe analysis to two dimensions.

Facts worth remembering -- Types of collisions

An elastic collision is one in which the total kinetic energy is the same before and after the collision.

An inelastic collision is one in which the final kinetic energy is less than the initial kinetic energy.

A perfectly inelastic collision is one that results in the two objects sticking together. The decrease of kinetic energy in a perfectly inelastic collision is aslarge as possible (consistent with the conservation of momentum).

Momentum is conserved regardless of whether the collision is elastic or inelastic.

A general solution for elastic collisions

I will provide you with three equations that apply in general to elastic collisions in two dimensions. However, as you will see, there are more thanthree variables involved in such collisions. With only three equations, you can only solve for three unknowns. Therefore, in order to solve the general problem,the values of all the other variables must be known.

The two-dimensional solution can be applied to one-dimensional problems by constraining the directions of motion of the two objects to either be the sameor to differ by 180 degrees. If possible, such problems should be structured to cause the directions to be along the x-axis. This will often simplify thesolution.

A general solution for inelastic collisions

The case for inelastic collisions is more restrictive than the case for elastic collisions. Only two of theequations mentioned above apply to inelastic collisions. As a result, you can only solve for two unknown values for an inelastic collision. The values for allof the other variables must be known.

Collision equations

The equations for collisions of two objects in two-dimensional space are shown in Figure 1 . Note that it is assumed that the two objects constitute an isolated system -- that is, a closed system that is not subject to externalinteractions. This requires that both the magnitude and the direction of the momentum for the system be the same at the beginning and the end of the collision.

Figure 1 . Equations for collisions of two objects in two-dimensional space.
Using conservation of momentum alone, we have two equations, allowing us to solve for two unknowns.m1*u1x + m2*u2x = m1*v1x + m2*v2x m1*u1y + m2*u2y = m1*v1y + m2*v2yUsing conservation of kinetic energy for the elasticcase gives us one additional equation, allowing us to solve for three unknowns.0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2 Velocities can be decomposed into their x andy-components using the following equations: u1x = u1*cos(a1)u1y = u1*sin(a1) u2x = u2*cos(a2)u2y = u2*sin(a2) v1x = v1*cos(b1)v1y = v1*sin(b1) v2x = v2*cos(b2)v2y = v2*sin(b2) Substitution yields the following for the two momentumequations: m1*u1*cos(a1) + m2*u2*cos(a2) = m1*v1*cos(b1) + m2*v2*cos(b2)m1*u1*sin(a1) + m2*u2*sin(a2) = m1*v1*sin(b1) + m2*v2*sin(b2) where:m1 and m2 are the masses of the two objects in kg u1 and u2 are the magnitudes of the initialvelocities of the two objects. Velocities are measured in meters/secondv1 and v2 are the magnitudes of the final velocities of the two objectsu1x, u1y, v1x, and v1y are the x and y-components of the initial and final velocities in 2D space.a1 and a2 are angles that describe the initial directions of the two objects through 2D space.Angles are measured counter-clockwise relative to the positive x-axisb1 and b2 are angles that describe the final directions of the two objects through 2D spaceIt is assumed that the two objects constitute an isolated system.Variables: m1, m2, u1, u2, v1, v2, a1, a2, b1, b2

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Daniel
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Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
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s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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