Understanding Newton's Second Law Through Plane Simulation

good morning today we'll be investigating the motion of this plane through this simulation

specifically we'll be investigating how mass acceleration and thrust are related to

each other now a force is any push or pull the thrust force is the main force that

is responsible for pushing the plane down the runway all forces are measured in the unit

called newton to give you an idea of how large a newton is when you hold a typical

apple steady you are exerting about one newton of force in addition to thrust another force

acting on a plane is called drag however in today's activity we are going to ignore the drag force

but there are other videos where we take the drag force into account so with our simulation we're going to

vary the thrust force and we're going to try to measure the acceleration while keeping the mass

steady these are the values we're going to use for our thrust

force let's see the simulation now here's our simulation our mass values 10 000 kilograms

and our thrust value is 100 000 newtons let's see what we get for acceleration ah first acceleration of the plane down

the runway is 10 meters per second per second we'll dial in our next force 120 000

newtons interesting the acceleration has increased as we've increased the thrust force

now it's 12. 140 000 newtons of thrust 14. you could almost guess

that for 160 000 units of thrust well the acceleration is 16. there does seem to be some sort of

connection between these numbers and finally for good measure 180 000 newtons of thrust

18 meters per second per second so here's our data table and let's plot this data thrust force on

the x-axis acceleration on the y-axis and let's try to determine an equation

for this line so we have the most general equation y equals mx

plus b but our y-axis is acceleration so we'll rewrite that as acceleration

equals mx plus b our x-axis is thrust

so we'll rewrite the equation as acceleration equals m times thrust plus b

m represents the slope of the line so we will draw the run and the rise for this line

and the run is 80 000 newtons how do we get 80 000 newtons well notice the run starts at 100 000 newtons and

ends at 180 000 newtons the difference is 80 000 newtons

the rise is 8 meters per second per second how do we get that well notice the rise

starts at 10 and ends at 18. the difference being eight

and so calculating slope slope remember is rise over run eight divided by eighty thousand

and we end up with this value for slope now substituting that value into the equation

we're almost there we're left with trying to figure out what b is and so how do we get b

well remember that b is the y intercept so we extend the line and notice that b is equal to zero

now this makes sense this is telling us that when the thrust is exactly zero newtons because that's

the x value the acceleration is also zero and so this seems to be our final

equation acceleration equals zero decimal zero zero

zero one multiplied by the thrust force exploring this equation in a bit greater detail now

notice that zero decimal zero zero zero one can be written as one over ten thousand

and so i'm gonna use that fraction in this equation and we have an acceleration equals thrust divided by

ten thousand hmm interesting going back to our simulation and you can rewind the video if you wish

the mass was 10 000 kilograms is there a connection between that 10 000

and the 10 000 in the simulation while there is the more general formula for acceleration

is that it's equal to thrust over mass for this specific simulation and in fact now regardless of whether

it's a plane taking off or any object experiencing a force the most general equation is that

acceleration equals force over mass so when there is more than one force

acting on an object we have to extend this equation acceleration equals net force over mass

so we use this equation when there's more than one force acting on an object which is very common

in everyday life and in physics problems what does that mean net means the sum

of all the forces acting on the object for our plane the net force was just the thrust force because that was the only

force that was pushing the plane down the runway this equation is formally known as

newton's second law and as you can see from the equation it

makes a prediction every equation in physics tells a story and if you understand the story then

physics becomes a lot easier so the story this equation tells is this

as mass increases acceleration decreases that's the story that this equation tells us

and this equation makes sense in everyday life if you've ever lifted an apple in a

bowling ball you know that the acceleration of an apple

will always be greater than that of a bowling ball because it's just that much lighter

in textbooks and in other sources this equation is also written as net force equals mass

times acceleration so how do we interpret what this actual equation means when written in this

format what story does this equation tell when written

in this format well imagine we had a one kilogram cube and imagine we want to accelerate

it at one meters per second per second in other words if this cube was

originally at rest after one second we want this cube to have a speed of one meter per second

that's what that acceleration means according to this law written by sir isaac newton

to accelerate a one kilogram object one meter per second per second requires a force a net force of one

newton and so i hope you've enjoyed today's explanation and example of newton's

second law have a great day bye bye