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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

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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LITNING Reply
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LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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..
Adin
why?
Adin
what school?
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.
Bharti
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Damian Reply
absolutely yes
Daniel
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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