A force of magnitude 7.50 N pushes three boxes with masses m1=1.30 kg, m2=3.20 kg, and m2=4.90 k

step 1 In this problem, we're going to talk about Newton's second law. So what we need to remember is t

A force of magnitude 7.50 N pushes three boxes with masses...

Key Concepts

Newton's Second Law

Newton's Second Law relates the net force acting on an object to its mass and the acceleration it experiences (F = ma). This fundamental principle is essential in analyzing the motion of objects, especially when multiple bodies are involved, as it allows one to calculate the acceleration of the system given an external force and, in turn, determine the forces acting on individual components.

Free-Body Diagram Analysis

A free-body diagram is a graphical illustration used to visualize the forces acting on a single object. By isolating each object and representing all forces (both external and internal), free-body diagrams facilitate the systematic application of Newton's laws to determine unknown quantities such as acceleration and contact forces in interconnected systems.

System Approach in Connected Bodies

When several bodies are in contact and move together as a system, it is useful to treat them as a single combined mass to determine the overall acceleration. This approach simplifies the problem by eliminating internal forces when computing the net force and acceleration, and later, these internal forces (contact forces) can be determined by analyzing individual components of the system.

Contact Forces

Contact forces are the forces transmitted between objects in physical contact. In a system where objects push or pull on each other, these forces arise due to the interactions at the interfaces. Determining the magnitude of contact forces involves applying Newton's Second Law to individual objects or subsystems, considering that internal forces are equal in magnitude and opposite in direction according to Newton's Third Law.

Transcript

00:01 In this problem, we're going to talk about newton's second law.

00:04 So what we need to remember is that newton's second law tells us that the sum of all the forces applied in an object is equal to the mass of that object times the acceleration.

00:18 Okay, so what we have in our problem is a setup with the three blocks that's shown here in the figure.

00:25 The first block one has a mass of 1 .3 kilograms.

00:29 The second one has a mass of 3 .2 kilograms.

00:32 And the third one, a mass of 4 .9 kilograms.

00:37 And a force, a horizontal force, is applied in block 3, such that all the blocks are pushed.

00:45 And the magnitude of the force is 7 .5 newtons.

00:50 And given this, our goal is to find what are the forces, the magnitude of the contact forces, between block 1 and 2, in question a, so we want to find f .2.

01:03 In question b, we want to know the contact force between blocks 2 and 3.

01:11 Okay, so the first thing we need to notice is that the total system has a mass that is equal to the sum of the individual masses, m1 and 2 and 3.

01:27 So it's 1 .3 kilograms plus 3 .2 kilograms plus 4 .9 kilograms.

01:34 So the mass m is equal to 9 .4 kilograms.

01:43 This is the total mass of the three blocks.

01:47 And the total force is 7 .5 newtons.

01:51 So this means that we can calculate the acceleration, that the force is the mass times acceleration, and the acceleration is 7 .5 newtons divided by the mass of 9 .5 kilograms, 9 .4 kilograms, i'm sorry.

02:06 So the acceleration is 0 .5.

02:07 0 .8 meters per second squared.

02:13 Let's keep this.

02:15 And with the acceleration, we're going to be able to find the contact force.

02:20 The contact forces actually between blocks 1 and 2 and 2 and 3...

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