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Solution for (a)

The first ball bounces directly into the wall and exerts a force on it in the + x size 12{+x} {} direction. Therefore the wall exerts a force on the ball in the x size 12{ - x} {} direction. The second ball continues with the same momentum component in the y size 12{y} {} direction, but reverses its x size 12{x} {} -component of momentum, as seen by sketching a diagram of the angles involved and keeping in mind the proportionality between velocity and momentum.

These changes mean the change in momentum for both balls is in the x size 12{ - x} {} direction, so the force of the wall on each ball is along the x size 12{ - x} {} direction.

Strategy for (b)

Calculate the change in momentum for each ball, which is equal to the impulse imparted to the ball.

Solution for (b)

Let u size 12{u} {} be the speed of each ball before and after collision with the wall, and m size 12{m} {} the mass of each ball. Choose the x size 12{x} {} -axis and y size 12{y} {} -axis as previously described, and consider the change in momentum of the first ball which strikes perpendicular to the wall.

p xi = mu ; p yi = 0 size 12{p rSub { size 8{"xi"} } = ital "mu""; "p rSub { size 8{"yi"} } =0} {}
p xf = mu ; p yf = 0 size 12{p rSub { size 8{"xf"} } = - ital "mu""; "p rSub { size 8{"yf"} } =0} {}

Impulse is the change in momentum vector. Therefore the x -component of impulse is equal to 2 mu and the y size 12{y} {} -component of impulse is equal to zero.

Now consider the change in momentum of the second ball.

p xi = mu cos 30º ; p yi = –mu sin 30º size 12{p rSub { size 8{"xi"} } = ital "mu""cos 30"°"; "p rSub { size 8{"yi"} } = - ital "mu""sin 30"°} {}
p xf = mu cos 30º ; p yf = mu sin 30º size 12{p rSub { size 8{"xf"} } = - ital "mu""cos 30"°"; "p rSub { size 8{"yf"} } = - ital "mu""sin 30"°} {}

It should be noted here that while p x size 12{p rSub { size 8{x} } } {} changes sign after the collision, p y size 12{p rSub { size 8{y} } } {} does not. Therefore the x size 12{x} {} -component of impulse is equal to 2 mu cos 30º size 12{ - 2 ital "mu""cos""30"°} {} and the y size 12{y} {} -component of impulse is equal to zero.

The ratio of the magnitudes of the impulse imparted to the balls is

2 mu 2 mu cos 30º = 2 3 = 1 . 155 . size 12{ { {2 ital "mu"} over {2 ital "mu""cos""30" rSup { size 8{ circ } } } } = { {2} over { sqrt {3} } } =1 "." "155"} {}


The direction of impulse and force is the same as in the case of (a); it is normal to the wall and along the negative x size 12{x} {} - direction. Making use of Newton’s third law, the force on the wall due to each ball is normal to the wall along the positive x size 12{x} {} -direction.

Our definition of impulse includes an assumption that the force is constant over the time interval Δ t size 12{Δt} {} . Forces are usually not constant . Forces vary considerably even during the brief time intervals considered. It is, however, possible to find an average effective force F eff that produces the same result as the corresponding time-varying force. [link] shows a graph of what an actual force looks like as a function of time for a ball bouncing off the floor. The area under the curve has units of momentum and is equal to the impulse or change in momentum between times t 1 and t 2 size 12{t rSub { size 8{2} } } {} . That area is equal to the area inside the rectangle bounded by F eff , t 1 , and t 2 . Thus the impulses and their effects are the same for both the actual and effective forces.

Figure is a graph of force, F, versus time, t. Two curves, F actual and F effective, are drawn. F actual is drawn between t sub1 and t sub 2 and it resembles a bell-shaped curve that peaks mid-way between t sub 1 and t sub 2. F effective is a line parallel to the x axis drawn at about fifty five percent of the maximum value of F actual and it extends up to t sub 2.
A graph of force versus time with time along the x size 12{x} {} -axis and force along the y size 12{y} {} -axis for an actual force and an equivalent effective force. The areas under the two curves are equal.

Making connections: take-home investigation—hand movement and impulse

Try catching a ball while “giving” with the ball, pulling your hands toward your body. Then, try catching a ball while keeping your hands still. Hit water in a tub with your full palm. After the water has settled, hit the water again by diving your hand with your fingers first into the water. (Your full palm represents a swimmer doing a belly flop and your diving hand represents a swimmer doing a dive.) Explain what happens in each case and why. Which orientations would you advise people to avoid and why?

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Physics of the world around us. OpenStax CNX. May 21, 2015 Download for free at http://legacy.cnx.org/content/col11797/1.1
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