Part 9 of 13 - Mathematical Expressions Dani asks Makena to...

Part 9 of 13 - Mathematical Expressions Dani asks Makena to write the expression for Newton's second law for $m_1$, using the sign convention as used in the simulation. Which expression is correct? $\sum F = T - m_2g = m_1a$ $\sum F = T + m_1g = m_1a$ $\sum F = T - m_1g = m_1a$ $\sum F = -T + m_1g = m_1a$

Transcript

00:01 So it's usually a good place to start with newton's second law is with a single particle.

00:07 And people usually learn to add forces that are working on that particle, with the result being equal to the mass of the particle times its acceleration.

00:20 And then you usually move on to systems of multiple particles, where there are a couple ways to handle such systems.

00:33 First of all, there is the way of breaking it apart into individual particles and then setting the forces on each particle equal to each mass times the acceleration of each.

00:47 And the downside to that is that you usually wind up with multiple equations and multiple unknowns.

00:53 So a second way to handle such a system is to treat it as all together with the sum of the masses equal to total.

01:02 Mass and the sum of external forces, not the internal ones, which are equal and opposite due to newton's third law.

01:19 So the internal ones act in pairs and third law pairs.

01:27 But set the external forces equal to mass total times the acceleration of the center of mass.

01:35 Now that acceleration of the center of mass is identical.

01:38 To the acceleration of the system, if the particles are all attached together and move together as a whole.

01:47 And those are usually the simpler things to handle.

01:51 So here we're going to take a look at an example of a system of two particles, and we're going to handle it in two different ways, both with the system approach and the break -and -apart approach.

02:06 So let's see.

02:07 Here we have, let's say, m2 that's going across some sort of surface, so there's friction.

02:21 And it is attached via a pulley and a string, lightweight string, to a mass one that is falling down.

02:38 We'd like to find the acceleration of that system.

02:42 So the first approach is the system approach.

02:49 The m total is equal to m1 plus m2.

02:58 We'll call the positive direction, the flow to the right of mass 2, and the flow downwards for mass 1.

03:09 And the forces acting externally are gravity on mass 1, so that's m1g, and friction on m2.

03:23 Okay, and we aren't going to worry about the string because the string is an internal force.

03:29 It's an interacting pair or it's causing the interaction between m1 and m2...

Question

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