Physics: Acceleration and the Pull of Gravity

So what's the relationship between acceleration and gravity? And where does velocity fit in? And who invited future velocity?

CoursesPhysics
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Transcript

00:41

well hello people I'm Isaac Newton without the annoying British accent and

00:46

I invented gravity okay okay it was actually just a theory that explains how

00:50

gravity worked and basically I figured out that everything that has mass

00:55

attracts everything else that has mass or to put it another way everything [Man and woman swining around]

01:01

attracts every other thing here on earth the biggest mass we've got is this the

01:07

globe that's why everything falls down toward

01:10

the center of the earth earth is the you know biggest thing around but what if

01:15

you're not standing on flat ground well let's say you're taking a hike up a hill [Woman hiking up a hill]

01:19

gravity is still pulling you toward the center of the Earth's core and since

01:24

you're on an angle on the hill this force isn't perpendicular to the ground

01:28

it's at an angle to the surface you're standing on the steeper the hill the

01:32

more acute that angle is but because we're on an incline that gravity is

01:36

broken into two components the first component is perpendicular to the

01:40

surface 90 degrees relative to the trail so that

01:43

component is pulling us straight down just like the gravity on a flat piece of [Gravity pulling woman towards earth's center]

01:47

ground well another component of gravity is pulling us parallel to the surface

01:52

which you're familiar with if you've ever rolled down a hill our lessons [Woman rolling down a hill]

01:56

lately have been all about acceleration why are we talking about rolling down a

02:00

hill well because gravity is a force of

02:02

acceleration it might take it for granted because it's always around you

02:06

might say it's constant because it is here on earth gravity is a constant

02:11

force of 9.8 meters per second squared now we can overcome that force by [Rocket appears]

02:17

providing a stronger force in the other direction like when a rocket launches

02:22

into space to get off the ground the rocket engines have to provide enough

02:26

force to achieve liftoff and it's the same thing when you throw a ball in the [Man throws ball in the air]

02:30

air your arm creates enough force for the ball to go upwards at least for a

02:33

little while it'll come back to earth eventually though when velocity and

02:38

acceleration are in opposite directions the velocity will eventually change and

02:42

turn in the direction of acceleration of course if velocity is strong an

02:47

acceleration is weak it might take a while to make that turn but if they're

02:51

both working in the same direction well unless another force acts on whatever

02:54

object is in motion the velocity will just keep on getting higher let's take a

02:59

look at how these forces interact well on this chart longer arrows indicate

03:04

greater magnitude than shorter ones and this is all about predicting the future [Velocity, acceleration and future velocity columns appear]

03:09

at least in the short term like we said over time acceleration will always

03:12

overcome velocity but as we can see with this set in the short term if velocity

03:17

is strong and acceleration is weak and they're acting in opposition while

03:22

velocity will be weakened let's look at how this plays out in a realistic

03:26

situation well the situation is that we're going to shoot a guy into the air [Newton puts a man into a cannon]

03:30

with a cannon look you have your reality and I have

03:34

mine the initial velocity will be 50 meters a second and we'll be pointing the

03:39

cannon straight up here's a graph of the guys displacement as he takes flight [Displacement graph appears]

03:43

well what does this graph tell us about the velocity well for one thing we know

03:48

he didn't have a constant velocity otherwise the line would be straight to

03:52

make a velocity time graph we need the slopes of the tangents to the

03:55

displacement graph we've already done that math and come up with this velocity

03:59

versus time graph right there remember if we see a linear graph for velocity it

04:05

means acceleration is constant acceleration is the change in velocity

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divided by the change in time well the final velocity here was negative 48

04:14

meters per second and the initial velocity was 50 meters per second making

04:19

the change in velocity negative 98 metres per second the time elapsed was

04:26

10 seconds so when we divide negative 98 m/s by 10 seconds we find an [Full equations appears]

04:32

acceleration of negative 9.8 meters per second squared magic see the

04:38

acceleration of gravity is constant gravity would never let us down well

04:44

true it actually always lets us down anyway everything so far has been [Man falling to the ground and Newton catches him]

04:50

theoretical I hate to let you down but we didn't actually launch some guy out

04:54

of a cannon all right well why don't we do some actual science that's right it's

04:57

lab time all right let's get our stuff together first we need a ball have a

05:01

ball tennis base golf any of those will do just fine [Newton with a selection of balls]

05:06

we need a way to measure height we can tape some paper to the wall and mark

05:09

measurements here or you can use an app here's one for the iPhone and here's one

05:14

for you Android users and we'll need a stopwatch which you might have on your

05:18

phone we'll be taking notes so you'll need paper on your computer or whatever

05:22

and we'll trust you can figure something out and last we'll also need to make

05:25

graphs well there's software for that and

05:27

there's old-school graph paper on three hit pause and go scavenge one two three [Newton with all of the items for experiment]

05:32

go.... all right got everything? awesome ish ideally this will be done as a team

05:38

we'll need someone who's throwing the ball and someone who's taking and [Girl with the ball and boy with stop watch]

05:40

recording the data so we need to get organized we need a grid that lets us

05:45

track the height of each toss and the time between letting the ball go and

05:49

catching it again and we'll eventually be figuring out the velocities for each

05:52

toss so include a column for that too and take a few practice throws make sure [Girl throwing ball into the air]

05:56

you can get a good read on how high the ball is going and you want to be as

06:00

consistent as possible in these tosses we don't want one throw to go two meters

06:04

high and another to go 12 high if for no other reason and when our ceiling isn't

06:09

that high and we want to throw the ball as straight up as we can don't worry

06:12

we're just human so we know there's gonna be some degree of error here...

06:17

Once you've gotten that toss down we can start doing this thing for real

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we need a minimum of three good tosses and if you've got a big group together [Girl tossing ball into air and group watches]

06:24

for this lab well take some more tries at it let everyone collect some of their

06:27

own data you can never have too much data ideally you'll be catching the ball

06:32

at the same height it left your hand otherwise whoever is working the clock

06:36

should try and stop timing when the ball returns to that same height if you make

06:40

a bad toss don't worry about it just don't include the data in that toss in

06:43

your chart we're gonna be doing some graphing now you know we're pretty

06:46

stoked too, can you tell? any graph we make needs a starting point well for a

06:50

displacement graph we can have a starting point at zero since the ball is [Displacement graph appears]

06:54

coming back to the same position it started from but what about velocity

06:57

well when we've seen velocity graphs before

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they've usually started with an initial velocity of zero but the ball is

07:05

already moving when you let it go so we got to figure out what the initial

07:09

velocity is all right good news we've got an equation for that here it is in [Initial velocity equation appears]

07:13

this equation the change in displacement which is that Delta X thing right there

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equals the initial velocity times the elapsed time that's the V sub zero thing

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and the T there plus one half acceleration aka A multiplied by the

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square of the time period that's the equation we know our change in

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displacement equals zero so we can put that into our equation and now we can

07:37

solve for initial velocity let's start by subtracting the last part of our

07:41

equation one half A T squared from each side leaving us with negative one half A

07:48

T squared equals V sub 0 times T now we can divide both sides by T to isolate

07:54

initial velocity so the initial velocity equals the negative of one half

07:58

acceleration times T our acceleration is negative 9.8 meters per second squared

08:04

and cutting that in half gives us negative four point nine meters per

08:08

second squared but we need the negative of that number so now we've got a [Acceleration formula appears]

08:13

positive number of 4.9 and since time will be in units of seconds we know that

08:19

will cancel out one of those seconds in meters per second squared and we'll have

08:24

the right unit for velocity so our starting velocity equals 4.9 times T

08:30

well it's important to remember that once the ball leaves our hand gravity is [Girl throws ball into the air]

08:34

the only force that's being applied to it even though it's moving up and

08:37

doesn't last very long so when we do our graphs for the data we collected we can

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be confident that the acceleration versus time graph will be flat which

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means the velocity versus time graph will be linear

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now let's do the graphs for each throw we made oh but before we do let's think

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of one more thing if we have our velocity correct and we have our time

08:57

period correct we can calculate the max displacement let's take another [Displacement graph appears]

09:01

look at our graph for cannon guy well we can see that this looks pretty

09:05

symmetrical right and the highest point with the most displacement is halfway

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through the journey there since velocity equals the change in displacement over

09:16

the change in time we can rearrange the equation to solve for displacement the

09:21

change in displacement equals the velocity times the time halfway through

09:24

the ball's whole journey but this is all in theory go ahead and find the

09:28

theoretical max height for some of your throws and compare that to what you

09:31

actually measure is the max height which do you think is more accurate do you [Recorded height and theoretical max height readings appear]

09:36

think you measured the height wrong did you not get the time quite right

09:40

throwing off the velocity again don't expect yourself to get any of this

09:44

perfect it's more important to be able to think through any errors we've made

09:48

okay for reals now put that pause button to use and get graphing compare your

09:52

graphs for each throw do they look like what you expected if you worked as a

09:57

team do your graphs look like those your colleagues drew and while we're thinking [Colleagues holding graphs]

10:01

about this stuff let's think about some other stuff too what determines how long

10:05

the ball is in the air what's the acceleration when the ball is stopped at

10:10

the peak of its arc and what do we have to eat around here [Tennis ball transforms into an apple]

10:13

okay well that last ones just means we're getting hungry so let's wrap this

10:18

thing up but yeah it's important to exert some

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brainpower on these questions there's no point in doing an experiment and taking

10:23

down data if we don't understand what it means and if you're feeling super

10:27

ambitious write up a whole report but for now it's snack time, oh an apple for

10:32

Isaac Newton yeah very funny [Boy gives Newton an apple]