This problem is about energy
and momentum; let's see what's happening. The block
of mass m1 is 2.5kilograms slides from height 10
meters on a frictionless surface. Good,
friction is 0. Whenever friction is 0 it's
easy because we can use conservation of energy...
and collides with a block of
mass, m2. So this is our m1, this is our m2.
And it seems mass m2 is at
rest, so there's no velocity... initial velocity for this.
V2i is zero. And, so the formulas are given
here. So we can go back when we do the problem and look at this
formula. Now let's see what is part A. Part A it says find the final
velocities of the two blocks after the collision if the
collision is elastic. Very good. When you say elastic you mean
that not only momentum is conserved,
not only momentum is conserved, I
can write for A,for elastic collision
I can say that both
total momentum
and total momentum...and
total kinetic energy
are conserved. That means they do
not change after collision. Conserve means remains the same;
they do not change. That means I
cannot put elastic collision, I can write that Pi, the total
momentum before is total momentum after, and also all
kinetic energy before is the same as all kinetic energy after.
So that's what you can say about
this. So if I replace the formula for
Pi and Pf andalso Ki, Kf
and solve for final velocities of
each object, we get to this formula, the two..
the formula that is given here.
So we have V1f, m1
minus m2, divided by m1 m2 times
V1i.And actually this formula is
true only V2i is 0.That means we can use this
formula for this problem. V2f is 2m1,
this is final velocity of the second object,
2m1, divided by m1 plus
m2 times V1i.I'm going to rewrite these two equations here again for
you to see what I mean.
So
here when two objects collide
and if we have V1ibut if V2i is 0 and the
collision is elastic,then I can write final velocity
of first object is m1 - m2 ... do you see that,
what you see here ... divided by m1 plus m2,
then times V1i, maybe
this is easier for you to see the formula and then replace
your numbers. And yes this V2fis, that means final velocity of the
second object, is 2m1 divided by
m1 plus m2, times V1i.
Okay so these are for elastic
collision; these are final velocities,
final velocities
in
an elastic
collision
when the second object is...when
the second object is
initially-
if my spelling is wrong-
initially
at rest.
Okay...it's initially at rest.
So these are the formulas weuse. Now you see that we can use
this formula for Part A. Its asking find the final
velocities of the two blocks after the collision if the
collision is elastic. Yes, we know m1 and we know m2
but how about V1i?
What is V1i...it's not giving in
the problem. but what happens actually what
happens here you see that's the one I is not give it when they
can find it we know that this M. this slice N. it ceases to this
point and then it's the second object
so leave on all I need is
velocity all of this blog and one before touching them to how
they can find the one on just using conservation of
energy on top here we have or the potential potential is in
one G. edge at the bottom here potential becomes zero all
potential converts to kinetic energy so hear Rihanna for me
one by falling on energy is just K. E. is every one one half
study one half in one V. is square listen me he is molasses
offers object before hitting the second object
which recorded the initial
velocity in that collision so we can use conservation of energy
and find V. of the blog before collision so I'm going to put
I'm gonna views right that so he said that initial energy is all
potential because it and one G. edge
this is part a
okay so we're trying to find
that and then again look at your final energy here chi
final energy here D. F. is K. E.
Mrs Vaughn half in one via square
but all the V. what a very fine
is I should do or V. one high so less calculated that so we put
our ego to eat F. alright is in one G. edge he F.
is one half and move on the square canceled and one and one
and then multiply by two you get
to cheat H. okay much braver to two G. H.
much bye bye to dis to register canceled so we have only this
code on this site no it's like our numbers CBS
could love to G. is nine point eight heights in the problem was
given what is high ten meters to see
that ten meters is hot so I can put heights here
ten square
so two times nine point is
nineteen point six nineteen point six times
hundreds so
then this becomes in nineteen
sixty so V. is a square root of nine is sixty
and this is where are the one
all I so from here V. one by
I just was just calculated is
for the four point two seven or
point three meters per second so good I have the one I
not the cabinet in the one I
forty four point three meters per second
so this guy could be one F. the
one F. is everyone minus and to
divided by in one place and to
then be one all by so this place this numbers and
one is two point five minus M. two is four kilograms
divided by two point five plus
four four zero so he then Vivek V. one by which is forty four
point three so such tract two point five
from four which is negative for
one point five
then time is it forty four point
three divided by six point five
so we need to talk with this
answer because we needed for not finding edge
this negative means what this
negative means actually months and one buses back after
collision and moved to the left and then it's rises up these
slide again so that was already one half
no V. two F.
is two in one divided by in one
place and to the to the one I again the same thing
so two times
and one is two point five
divided by six point five which
was a some of these two bedrooms five divided by six point five
meters per second that's only two F.
okay so they calculated the
final velocity of each blog after a collision
okay this was for a last look at
tennis go back to the problem said that's for elastic part
eight point the final velocity of the two boys after the
collision if the collisions elastic
nobody is saying find the final
velocities of the two blocks after the collision if the
Christians the LST so if he's the last seat you can
not use this for me does that V. just had four elastic equation
for in it as a collision what
happens it means that if I could see that is the slide
and this must in one slide down
and
the lawsuit velocity of forty
four point three meters per second we just calculated
and he's the second object
so this is a must and won't
and this is mass into another
this stick together it says that this is in elastic
that means they moved to get it if they move to get their means
final velocity is the same for both of them because they're
moving to get that is in LST collision
so now our mass is in one place
and to the
I I need to use conservation of
momentum I say initial momentum should be the same as final
moment initial momentum of this blog
everyone is everyone the one I the second broad was outrageous
into the two all right and this is zero
their final moment on the two
objects move to get there so is and one person two times the the
final so from here we can find
finalists of the two blocks after the collision then the
collisions in elastic that means the stick to each other so V. F.
I can solve for the ever just
plug numbers and now I'm just putting this we
want everyone vivant by divided by and one plus and to
everyone is two point five
the one is forty four point
three then the sum of the two masses
was six point five from here we can find dances in meters per
second but the very sensitive so you can plug in numbers in
calculated so and Catholic
not that was parked be
okay
and that actually does on
numbers for port eighty so for parts see
let's see what his ****
US to find what is the maximum
what is the maximum height to reach everyone rises after the
collision I need to put elastic collision because this happens
only for part of a so what is the maximum height to
reach and water rises after the last two collision
so what does that mean so that
means it bounces back it goes up and is of some that
if I read your this and that
means this is what's happening here I have this
okay the this is
this is M. won't
with his final velocity V. one
is going to the left so is going up
Ernest of summer here everyone
so if you're looking for these heights good looking for his
heart from what the heights to what height it can arise
okay so I'm looking for this
site we use conservation of energy
again initial energies old
Kinnitty final energy is all potential
okay
if is all
potential
and kinetic energy is all new
show so that's what we have initial and find
one more time you have done this
many times I easy F. R. E. I. is K. E.
E. F. is you you
RJ is is one half in one V. one
FS square remember
the them this happens after a
collision with the second object so I need to put V. one F. is
square then in one G. edge again cancelled everyone in one you're
looking for high that means we divide the two sites by
G. H. is V. one FM squared
divided by two G. the one F. as square remembered
that he had put it fits here is this number
we'll show you the one F. is
this number calculate this number using calculators
and this
plug it here okay so you have
with this system
you have the one F.
how could this number after you
have the answer forget here times two two times nine point
eight you get the high the US to find in the
pub thank

PHYS1401, physics, Shahnaz Sokhansanj, Practice Exam 2, Question 5

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