Boxes A and B are in contact on a Horizontal, friction less surface, as shown in Fig. E 4.23 . B

Boxes A and B are in contact on a Horizontal, friction less...

Key Concepts

Newton's Third Law

Newton's Third Law of Motion indicates that for every action there is an equal and opposite reaction. This law is crucial when analyzing the forces between contacting objects since it ensures that the force one object exerts on another is met with an equal and opposite force, maintaining a balance of forces during the interaction.

Contact Forces

Contact forces arise when two or more bodies are in physical contact and exert forces on each other. These forces are internal to the system and are necessary to ensure that the objects move together. Calculating contact forces involves applying Newton's laws to individual bodies and ensuring that the acceleration determined from the net external force is consistent across all objects.

System Approach to Dynamics

The system approach involves treating multiple objects that are in contact or connected as one combined body to determine a common acceleration under an external force. Once the common acceleration is known, the internal (contact) forces between the objects can be analyzed individually, which is particularly useful in problems involving multiple bodies sharing the same acceleration.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). This principle is used to determine the acceleration of a system when multiple forces are acting and is fundamental in connecting the applied forces to the resulting motion of the objects involved.

Transcript

00:01 All right, chapter four, problem number 23, we got two blocks and side by side.

00:05 We're pushing with 100 newtons on the bigger block on the left -hand side.

00:09 And they want to know what is the force that the smaller block pushes on the bigger block with.

00:14 And the key here is going to be drawing correct free body diagram.

00:17 So let's start with the 20 -kilogram block.

00:19 That dot represents the 20 -kilogram block.

00:21 The force is acting on it are mg going down and the normal force going back up.

00:28 That block's not accelerating vertically, so those are, equal.

00:31 We're pushing on that block with 100 newtons of force to the right.

00:35 The 5 kilogram block is pushing back to the left.

00:39 And let's call that the force from block.

00:42 Oh, i can't remember what they named these guys.

00:44 I believe this is a and this is b.

00:47 So let's call the force on a from b.

00:51 Right.

00:52 Now, the key to understanding this problem is a free body diagram also for what's going on with the 5 kilogram block.

00:57 Okay, because i know there's a newton's third law.

01:00 Pair here.

01:01 So yeah, we've got the weight going down here.

01:03 We have a normal force going up here.

01:06 And then we're going to have the force from b on a.

01:10 Let me draw that a little bit better because i know that this is an action -reaction pair.

01:14 So the force of b on a.

01:18 So let's see here.

01:22 Those forces are equal in opposite.

01:23 So force a -b is equal to force b.

01:30 One of them, we can find either one, because the magnitude of the force is going to be the same.

01:35 So looking at newton's second law over here for block b, the net force acting on block b in the x direction is equal to the mass of block b times its acceleration in the x direction.

01:47 The only horizontal force acting is that force b, and that's going to equal the mass of block b, which was given us 5 kilograms, times its acceleration.

01:58 Now, we know the mass, but unfortunately, we don't know the acceleration of either block.

02:02 I know that they're going to have the same acceleration.

02:05 So we actually have to find the acceleration first.

02:09 So i'm going to use a trick...

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