Boxes A and B are in contact on a horizontal, frictionless surface (Fig. E4.23). Box A has mass

Boxes A and B are in contact on a horizontal, frictionless...

Key Concepts

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). This principle is crucial for calculating the acceleration of systems and determining the net forces acting on individual components within the system.

Newton's Third Law

Newton's Third Law asserts that for every action force there is an equal and opposite reaction force. In the context of interacting objects, such as boxes in contact, it explains that the force exerted by one object on another is matched by an equal force in the opposite direction, vital for understanding the interaction between the boxes.

Free-Body Diagrams

Free-body diagrams are graphical representations used to illustrate all the forces acting on a single object. They are an essential tool in physics for breaking down complex systems into simpler parts, allowing for a clear visualization of how forces such as applied forces, friction, or reaction forces act on different components.

System Approach in Dynamics

The system approach involves analyzing multiple interacting objects as a single entity to determine the overall acceleration under external forces. Once the acceleration is known, the internal forces between the objects can be isolated and determined, simplifying the analysis of variable interactions within the system.

Transcript

00:01 Okay.

00:01 And this problem, we have two blocks that are side by sign one another's thie ground.

00:09 We have block a on the left right here on the block.

00:13 B is a little bit smaller, and it's on the right right there.

00:17 And they were being told that some exterior applied force is being ah, applied on block a.

00:27 I'm sorry, actually going, tio, draw two separate for your body diagrams for this problem.

00:33 Just in order to better understand what is what is going on.

00:36 I'm starting off with block a.

00:40 So, of course, the first force that we're going to include in their is the applied force we want to think of it is being applied on the sensor of massive block a, which is in the sensor right there on the moving over teo block b on the side over here because they're in contact with one another.

01:01 Block a is exerting a force on block b on.

01:05 We're going to call that f a b.

01:09 Because block a is exerting a force on block b hover loosens.

01:15 Their law dictates that every force has an equal and opposite reaction force.

01:22 So in turn, the opposite direction of block b is going to be exerting a force on block a and is going to look a little something like that that completes our three body diagrams for this problem from's.

01:37 Now let's go ahead and applying it in second monte to the blocks.

01:41 Um, and when you sum of the forces on block a.

01:45 So if we set up our coordinate system so that x is increasing a ce, we go to the right.

01:53 Then we can say that if we subtract off fda from at that walk, give us a positive force in the end.

02:01 Oh, and then we end up with the massive parquet anymore supplied by the acceleration.

02:09 That's the key here.

02:10 Is that the blocks on contact one another.

02:12 So one last requirement we have is that the two blocks air moving at the same accelerations.

02:18 In other words, a is equal to a beam, so it's just going to find that to be the same acceleration on then, sir, it's some juice over here, something new since second law looks like for block a, what does it look like for block b? while the only force that's being exerted is f of am being simply going to be equal to the mass of block being multiplied by that acceleration that we define, which is just lower case, eh? was no, um, subscript so now it can combine.

02:53 These two equations wants do that over here.

02:56 Basically, the two a's are equal to one another.

03:00 So let's go ahead and highlight those stuff.

03:03 We do some rearranging.

03:07 Easiest way to do that would be to rearrange this expression on the right here and say that acceleration is equal...

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