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## Pixar in a Box

### Unit 7: Lesson 2

The physics of particle systems- Start here!
- Graphing motion over time
- Position, velocity and acceleration
- Vector addition
- Velocity and acceleration vectors
- Understanding net forces
- Net forces
- Force and acceleration
- Applying gravity to a particle
- Particle collisions
- Particle collisions
- Animating particles
- Particle calculations

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# Force and acceleration

What's the different between a wind force and the force due to gravity? This video covers both Newton's second law of motion and law of gravity.

## Want to join the conversation?

- At1:41, Matt mentions that Newton came to the conclusion that not only force was proportional to mass times acceleration, and that Newton proved that force is EQUAL to mass times acceleration. How did he figure that out?(12 votes)
- We simply define the Newton (N) such that the constant of proportionality is 1. If we wanted we could define a different unit and introduce a proportionality constant, but what would be the point.

However it is worth noting that because we have definied the proportionality constant as one here, this restricts our representation of other equations like Newton's gravitational force equation between two masses, where a constant called G has to be added in to make the gravitational force consistent with the force of acceleration the masses experience.(3 votes)

- who here died on the inside at3:02(8 votes)
- if you rolled the balls down a hill, which one will accelerate faster?(3 votes)
- 2:15Galileo also did this experiment, and found that the heavier ball rolled faster.

(He used his heart rate to measure it, so he might have got excited and his heart sped up... XD).(4 votes)

- in the video the persons talked about newton`s laws. I remember Albert Einstein made some changes to Newton's laws. Does this changes anything or am i mistaken.(4 votes)
- At1:26it states that "a~f/m". If I would substitute the "f" in the equation by "a" (since they are proportionally the same) it shows an incorrect equation "a~a/m". Can someone tell me why the equation "a~f/m" is true, or what am I doing wrong?(3 votes)
- Why did both the balls which were thrown towards the ground from leaning tower of pissa fell with same acceleration? (Newton's experiment)(3 votes)
- They were dropped, not thrown. Also, they have the same acceleration because the acceleration due to gravity is the same for all objects. He explained why in the video, but I'll try to explain a little differently.

1) An object with more mass is harder to move than an object with less mass.

This means that an object with more mass requires a greater force to move it. So, picking up a plate is easier than picking up a monitor.

2) When it comes to gravity, a larger mass is affected by gravity more strongly.

For instance, the force that the Earth exerts on you is much less than the force that the Earth exerts on the moon.

Facts one and two (sort of) cancel each other out, so you end up having all objects fall at the same acceleration due to gravity (assuming that we do not take air resistance into account).(1 vote)

- 0:40I Wonder Why There Is Wind Force On An Atomic Level? Wouldn't That Just Be Oxygen Hitting The Particles?(3 votes)
- wow this is craaaazy

i feel like i need to lie down(2 votes) - in the equation F = mg, what is F? Did it say and I just missed it?(1 vote)
- Actually, big 𝐹 represents the force of gravity. (FORCE, not acceleration!)(2 votes)

- More aceretly each mass have different things(1 vote)

## Video transcript

- Welcome back. So now we know if a net
force is acting on a particle then it will accelerate in that direction. By how much will it accelerate? To answer the question of
how force and acceleration are related, Newton observed
that if you increase the net force by, say, a factor of two, then the acceleration
increases by that same factor. This means that force and acceleration are proportional to one another. But that's not all that matters. Next, let's consider the
mass of our particle. Imagine we have two
particles floating in space, which are the same size
but have different masses, like if one is a ping pong ball and the other is made of lead. If we applied an equal force, like wind, to both particles, what would happen? Both particles would
experience the same net force in the direction of the wind, but they wouldn't
accelerate at the same rate. The less massive particle,
the ping pong ball, would accelerate faster
than the one made of lead. So less mass results in more acceleration and more mass results
in less acceleration, meaning that mass and acceleration are inversely proportional to one another. And we already know that acceleration is proportional to force. Putting these together we see that acceleration depends on
the magnitude of net force, which is proportional to acceleration, and the mass of the object, which is inversely
proportional to acceleration. This gives us a is
proportional to f divided by m. Multiplying both sides by m gives m times a is proportional to f. And if we flip this, we get f
is proportional to m times a. Newton found that f isn't
just proportional to ma, it's in fact equal to ma. This is Newton's second law, f equals ma. To recap, f is the net force
acting on the particle, m is the mass of the particle, and a is the acceleration of the particle. Now let's consider the force of gravity. You made have heard of the famous story about Galileo's experiment in 1589, where he dropped two balls
off the Leaning Tower of Pisa. One was made of a light material, the other a heavy material. You might be surprised
to know that he observed that the two balls accelerated
at exactly the same rate. That blew everyone away. At the time, everybody, starting
with the ancient Greeks, just assumed that heavier objects fell faster than lighter objects. So unlike wind, the force of gravity seems to be independent of mass. The interesting question is why. Newton gave us the answer. His first law of gravity said
that more massive objects experience greater gravitational force and his second law says that mass is a resistance to acceleration. These two competing trends,
one encouraging acceleration and one resisting it,
cancel each other out. To see why this happens mathematically, Newton theorized that force
due to gravity, call it big F, is proportional to the
mass of the particle. Big F is proportional to ma. Think of gravity as an
acceleration vector, call it g, such that big F is equal to mg. So we have two equations. Newton's second law,
little f is equal to ma where little f is the net force and Newton's law of gravity
where big F is equal to mg. For a particle being
acted on by only gravity, the net force little f is big F. Little f is equal to mg is
equal to big F is equal to ma. Or more simply, mg is equal to ma. Notice the m cancels,
leaving just g is equal to a. That is, the acceleration of a particle, when acted on only by gravity, is independent of the
mass of the particle. This is why objects of different
mass fall at the same rate. An equation like this one, that allows us to compute the acceleration of particles, is called an equation of motion. We've covered a bunch of new and important concepts in this video. So let's stop here for some practice, using the next exercise.