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Teachers & SchoolsIt's experiment time. We'll be rolling a marble down a ramp... and we'll see what it tells us about gravity, acceleration, and velocity.

Courses | Physics |

Language | English Language |

gravity. Now that may not sound too impressive today, but he did all this

science, in the 1500s. He didn't have any fancy computers, or a smart phone to [Galileo in different rooms experimenting]

record stuff, or YouTube to watch videos of dogs and monkeys being best friends.

Nope, he had to figure out a simple way to measure gravity. So what he did was

set up a ramp, roll the ball down it and timed how long it took. And he did this

experiment hundreds of times. Because again no YouTube, what else was he going

to do all day. What did he find? Well for one thing, he found that each time he did

the experiment, when the ball was halfway through the trip, in terms of time. It was

only one quarter of the way through it, in terms of distance. So the ball covered [Galileo rolling experiment]

three quarters of the distance, in the last half of the roll. He also learned

that the angle of the incline, directly correlated with the speed of the ball at

the bottom of the ramp. In fact the acceleration equalled the

force of gravity, times the sine of the angle of inclination.

Oh yeah, consider this a warning, in this lesson we'll be getting our trigonometry

on. Galileo also found that the ball, would continue to travel horizontally, at

the same speed, as when it left the ramp and that speed would stay constant until

something stopped it. Like hitting a wall, or falling on the Galileo's foot. Well

we're gonna be doing an experiment of our own, in just a minute, that's kind of [atom talking]

similar. But let's make sure we're clear on the math, first. In our other lessons

we've used the acceleration of gravity, as 9.8 meters per second, squared, as our

only form of acceleration. However since we'll be dealing with an

incline, we can't use gravity, because we're not dealing with freefall anymore.

So the first thing we have to do, is to calculate the correct acceleration, using [atom talking]

that equation, we just mentioned. This one rod chair. Well once we have that

acceleration, we're able to find the final velocity.

Remember this equation, that one. It tells us that the square, of the final velocity,

equals the square, of the initial velocity, plus two times the acceleration,

times the change in displacement. In this case the change in displacement will be

the length of the ramp. Oh and all of this motion is in the horizontal [ramp with equations]

direction. Which is why we've got all these X's. Once we have that final

velocity, it becomes the speed of the ball as it leaves the ramp and then? Well

then we can predict the future. Not at tomorrow's winning lottery numbers kind

of prediction. More of a here's where a marble will land, when it rolls off the

table, kind of prediction. Okay well let's get our lab set up. First we need

equipment. We need some small dense ball like a marble, or maybe something metal.

As long as it's not bouncy, we should be just fine. Next up, a table and we mean an

actual table this time, not a data table. Some kind of smooth surface that we can [ball rolling on table]

roll the ball off of. Yep it could be a counter top, or the top of the dresser.

Next up a measuring tape, or a ruler, or a meter stick. Well we want to be using

metric measurements, but a worse comes to worse, we can always convert. And

if you're making a conversion, just know, that one inch equals 2.54 centimeters.

Then we need something to make our ramp. Now if you already have some sort of

ramp like thing, like maybe an old triangular wooden block you used to play

with, or a piece of Hot Wheels track, well then feel free to use that. We're [man being snob in empty room]

not gonna be ramps snobs. Just make sure that angle isn't too steep. Nothing more

than 30 degrees. Otherwise see if you have some heavy cardstock, or some

lightweight cardboard, something like that. We can DIY our own ramp out of that

stuff, and pen, paper, scissors and tape. Oh and also we might want to use a plumb

bob and no it's not a guy named Bob, who can unclog your bathtub. A plumb bob is a

weight, that hangs straight down from a string. This weight will let us find exactly

where the edge of the table is on the ground. We just hang our plumb bob from[atom doing experiment]

the end of the table, like this. It takes some guesswork out of determining where

the freefall will start. And last, but never least, we need a calculator. An

actual calculator, a calculator app, something on a webpage, whatever, okay. Now

we need to put everything together. Make sure the table is level, set your marble

down and see if it rolls to one side, or another.

If it does, put some paper, or something under one of the tables legs. Help set it

straight. If you need to make your own ramp from the cardstock, or cardboard,

well and go ahead and do that now. We're gonna leave this feat of engineering to

you though, all on your own. Just figure out some way to make a stiff ramp, that's

pretty shallow. This isn't a scary waterslide we're building, we want just a[man on resort water slide]

fairly gentle roll. So here's the plan we're gonna set up our ramp at one end

of the table. We'll let the ball roll down it. Then on the other side, when the

ball falls off the table. We're gonna mark where we think it will land. So how

do we figure out that landing spot? Well first it might help to draw a little

diagram of what we're working with. The ramp, the table and the floor for

starters. Then measure the length and height of the table, go ahead and write

those measurements down on the diagram and we need to measure the ramp to, the

length, height and hypotenuse. And yeah write those measurements down, we don't [measurements of experiment]

want to forget them. While we're doing all these measurements, figure out how

tall you are. Has nothing to do with the experiment, it's just you know good to

keep track. All right well with the measurements of the ramp, we can

calculate the angle of the incline. Remember sohcahtoa, no it's not an

ancient druid chant. It's a way to remember trig functions. We'll just look

at the SOH part. That tells us that the sign of an angle, equals the opposite [equations on chalkboard]

side, over the hypotenuse. Which would be helpful if we knew the angle already and

knew the length of one of the sides. Yeah, then we could find the length of

whichever side we didn't know. Well in this case we know the length of both

sides. We don't know the angle, which means we need to break out the inverse

function of sign. Well ladies and gentlemen, please welcome back to the

stage, the arc sign. Ya, the arc sign is kind of the opposite of the sign. So if

sign x, equals y, arc sign y, equals x. Now make sure your calculator is set for [calculator preforming functions]

degrees and for the inverse of functions. Then find the arc sign of the length, of

the opposite side, divided by the length of the hypotenuse. Because we know

the lengths of each side, we can use any of the inverse functions, arc cosine, arc

tangent, pick your poison. And slap that number up on the diagram too. Okay almost

time to look into our crystal ball. But we have to calculate our velocity first.

Step one, acceleration. Which equals gravity times, the sign of the angle of [formulas on chalkboard]

incline. The gravity is always, 9.8 m/s^2 because, we're on earth. Let's

say that we happen to have, a perfect 30-degree angle of incline. When we put

that number in, we find that our acceleration equals 4.9 m/s squared. And

then we need that final velocity. First let's figure out the horizontal velocity.

The square of the final velocity, will equal the square of the initial velocity,

plus 2 times the acceleration, times the change in displacement. Our initial [atom talking and chalkboard equations]

velocity will be 0. So that makes things a little easier and let's say the ramp

is 20 centimeters long. We want our velocity to be in terms of meters per

second though, so we'll call it 0.2 meters. So we double our acceleration,

making that 9.8 meters per second squared and we multiply that

acceleration by, 0.2 meters. Which means that the square of the final velocity

equals 1.96 meters per second. And when we find that square root, to solve for [formulas on chalkboard]

the velocity. We get 1.4 meters per second. Well now we have to figure out

how long it'll take this ball, to fall to the ground, after it rolls off the table.

Which means it's time for another equation. We're sure you remember which

one to use. Which is good because we don't. Oh yeah, now it's coming back to us.

We'll use this one, the final displacement, equals the initial

displacement, plus the initial velocity, times the elapsed time, plus 1/2

acceleration, times the square of the time. Our final displacement will be, the [equations on chalkboard]

height of the table and our initial displacement will be, 0. Our initial

velocity will be 0, just standing there, because you know, right now we're just

looking at this vertical velocity. Forget about all that horizontal junk, we were

looking at before. Well don't actually forget it, we'll need it in a minute. With

those two values, equaling zero, we're left with this, the height of the table,

equals 1/2 the acceleration. In this case gravity, times the square of the time and

that time, is what we need to solve for. Time to rearrange the furniture, in this [atom talking in classroom]

equation. Well we'll start by multiplying both sides by 2, then we'll divide both

sides by the acceleration and don't forget to find the square root of each

side also, so we can get all the way down to plane

T. So the square root of two times the displacement, divided by the acceleration,

equals the time. If we say that the table is one meter tall and plug in the

numbers, we'd find that the time equals 0.45 seconds. A little longer than the

blink of an eye. So keep those eyes peeled, we don't want to miss anything. [atom talking with red background]

All right now we're ready to make a prediction. We have our horizontal

velocity and we know how long the ball will be in flight. Multiply those two

numbers and we'll have the horizontal distance, aka the range. Go ahead and

write that value down as the predicted distance. And measure out that distance

from the edge of the table, putting that plumb bob to use, if necessary. Now tape

your paper down, so it's centered. You know, where you expect the ball to land.

Go ahead and draw a line across the paper, of that predicted distance, good.[atom setting up experiment]

Experiment assembly is officially complete, time to get the ball rolling. Go

ahead and place your marble at the top of the ramp and let that bad boy get

going and hustle over to see where it lands. Make an X, at that landing spot.

Then measure the shortest distance from that spot, to the line we drew earlier.

That distance, if there is one, is our experimental error. Feel free to run the

experiment a few more times. Go ahead, don't be shy, more data is always good.

Besides it took a lot to set all this stuff up, so like let's amortize it, a [atom talking with blue background]

little bit people. All right, yeah. Okay, all done? Did we get it right? If not

well and we had some experimental error. Well what what might have gone wrong? Was

the table not as level as we thought? Did the ball hit a stray cheerio as it

rolled? Did our sister start talking, creating a sudden gust of wind, that blew

the marble off course. And what was our actual horizontal velocity? We can

calculate that vector, by finding our actual change in horizontal displacement

and the time, to figure out how fast the ball was going when it fell off the

table. And how about this question, which would be more accurate? Calculating the [atom running experiment]

expected time the ball takes to fall to the floor, or using a stopwatch to

measure it. Well thanks to our good buddy Galileo, or the big double G, as we like to call

him. We know just how strong gravity is. Without that knowledge, we wouldn't have

been able to do this experiment at all. Now some of Galileo's later work got him

in trouble. In fact his insistence that the earth isn't the center of the

universe, got him placed under house arrest by the Catholic Church. But I

promise, stick with me and the Spanish Inquisition won't come knockin at your

door.[Galileo wondering halls]