## Ballistic Pendulum Lab with data

[Music]

good morning students

hope you're all safe at this time we

have had to move all the courses online

including the labs and so I'm trying to

make videos for each lab and hopefully

it'll give you something close to a

real-time experience okay so here is the

ballistic pendulum lab you've actually

used this equipment before but you've

not used the pendulum part so in the

ballistic pendulum you have a pendulum

and it's quite a heavy one that's why

it's called ballistic it's a heavy

pendulum hanging there and then behind

it you have a protractor that can

measure the angle you see this black

lever it needs to be pushed all the way

to the zero mark but when the pendulum

is hanging vertically the angle is zero

with the vertical and initially the

pendulum is lifted up and a steel ball

is pushed into this slot using a plunger

and the steel ball is pressed against a

spring so that when you pull that

trigger which you you can see it on top

here using that string when you pull the

trigger the ball is shot out at a

certain velocity and before you shoot

out the ball the pendulum is brought

back to this vertical position the lever

is pushed back to zero and then you pull

the trigger the steel ball flies into

that pendulum and gets stuck in it and

together the pendulum and the ball swing

up through a certain maximum angle and

of course it'll drop down after that but

the level will stay there showing us the

maximum angle through which the pendulum

swung through okay so here we have that

in the diagram when you pull the trigger

the pendulum swings up and goes to this

maximum position and so the lever is now

showing a certain angle okay

so that's all that we need to do in this

lab and we got to repeat this ten times

and take the average value of the angle

using the average value of the angle and

some other quantities we can calculate

the velocity with which the steel ball

was ejected out of that gun now here is

the data that you will be using in this

lab here are the 10 trials these are the

angles and then the average angle is

fifty point nine degrees so you get the

average angle then the pendulum is taken

off from the hook actually it can be

removed from here using this screw it's

taken off and the length of the pendulum

is measured the length of the pendulum

also the mass of the pendulum is

measured so you have the length of the

pendulum and the mass of the pendulum

another quantity that we need is the

mass of the steel ball okay so those are

the quantities that are given here the

length of the pendulum is 0.3 meter

which is 30 centimeters and that's the

length to its center of gravity not to

the bottom to the center of gravity

which will be the center of the hole

into which the ball goes and then of

course that's the average angle and here

you have the mass of the pendulum which

is 139 point three eight grams remember

to change it into kilograms when you

calculate also you have the mass of the

ball now using these quantities I'm

going to show you how to calculate the

velocity with which the ball came out of

the gun cut so now let's get to the

calculations so here you have the final

position of the pendulum after

swung through a certain angle coming up

there and then initially remember it was

in the vertical position and when the

angle was zero with the vertical so the

ball is now stuck in the pendulum but

before it's just an empty slot for the

ball to get stuck into and here are the

quantities the little m is the mass of

the ball the velocity with which it's

coming out is the little V there the

mass of the pendulum is Cape's M and V

subscript F is the final velocity now

that's an important quantity is the

velocity with which the pendulum and the

ball together begin their upward swing

okay that that's the important quantity

so after the ball gets stuck in the

pendulum they together have an initial

velocity with which they swing up and

then you know the final velocity becomes

zero

so whatever kinetic energy they both had

at the bottom is transformed into

potential energy at that position so

we're going to use the conservation of

energy in this case and also the

conservation of momentum okay so also

look at the height the height through

which the pendulum swung up is H and

that can be calculated from the angle

theta simply using thread in this right

angle triangle so I'm not going to go to

how we get that but basically we can

calculate that but before that here is

the conservation of momentum

ohright this is the initial momentum of

the ball mass times velocity is momentum

you know the initial momentum of the

pendulum is zero because initially it

was not moving it was at rest so that's

the total initial momentum and then the

ball got stuck in the pendulum so the

total mass is now M plus caps M

and then their velocity which is the

same for both because they're together

is we sub F so the that's the final

momentum now according to conservation

of momentum the initial momentum is

equal to the final momentum so that's

here all right now let's apply the

conservation of energy like I told you

the initial kinetic energy of both of

them as this swing up which is one-half

times the total mass multiplied by VF

squared is equal to MGH

because potential energy is mg H you

know that these two quantities will

cancel out right we'll do that in a

second but remember I told you from the

trig here you can calculate the H using

this formula H is L minus L cosine theta

so that's the first thing you will do

from the average value of theta knowing

the length of the pendulum which I've

given you you will first calculate the

height the height through which the

center of gravity of the pendulum swung

up once you get the height you will put

it into this formula and calculate VF

like I'm showing you because you see

these two cancel out and then bring the

two to the other side and take the

square root you get VF is square root 2

gh so once you get H you can calculate

this finally once you get that put it

back into conservation of momentum and

calculate the velocity of the ball the

initial velocity of the ball and here is

the form all right so that should make

sense so there are three things that you

need to do number one calculate the

height from the angle number to

substitute that height and calculate VF

number three

put that VF into this formula rather and

calculate the velocity of the ball so

the aim of this experiment is to

calculate the velocity with which the

ball comes out using the principles of

conservation of momentum and

conservation of energy so that is your

lab now how I think you should be able

to turn in a lab report so the document

is already posted on blackboard you can

look at the document get these data into

those tables and turn in a lab report on

blackboard as you normally do remember

there should be a cover page and all the

other things including a conclusion and

it should be a single attachment and

turn it in before Saturday midnight so

this is how I hope we can do the labs

going forward I know it's not exactly

the same as you doing it but under these

conditions this is the best that we can

do so I hope you understand this this is