(II) Calculate FA and FB for the uniform cantilever shown in Fig. 9-9 whose mass is 1200 kg.

Name: Problem 10, Chapter 9: Physics: Principles with Applications
Uploaded: 2019-06-04T23:33:49-08:00
Duration: 11 min 24 s
Channel: Paul A.
Description: (II) Calculate FA and FB for the uniform cantilever shown in Fig. 9-9 whose mass is 1200 kg.

step 1 So once again, welcome to a new problem. This time we have a can liver, and it's stretching acro

(II) Calculate FA and FB for the uniform cantilever shown in...

Key Concepts

Static Equilibrium

Static equilibrium is a core concept in mechanics where all forces and moments acting on a structure balance out to zero. This principle allows us to analyze a system by ensuring that both the sum of all horizontal and vertical forces, as well as the sum of all moments about any point, are equal to zero, thereby confirming that the body remains at rest.

Uniform Beam

A uniform beam is one in which the mass is evenly distributed along its length. This uniformity simplifies the analysis since the weight per unit length is constant, and the equivalent point load, typically acting at the beam's midpoint, can be used when summing forces and moments.

Center of Mass

The center of mass of an object is the point at which its mass can be considered to be concentrated. For uniform bodies, this point is geometrically in the center, and it is crucial in static analysis because gravitational forces can be assumed to act at this point.

Reaction Forces

Reaction forces are the forces exerted by supports or connections that balance the loads applied to a structure. In static systems, these forces are determined by applying the conditions of equilibrium, ensuring that the net force and net moment are zero so that the structure remains stationary.

Cantilever

A cantilever is a beam or structure that is fixed at one end and free at the other. The analysis of cantilevers involves considering both the support reactions at the fixed end and the effects of the distributed load due to the beam's own weight. The fixed end typically provides both a reaction force and a moment to counterbalance the load.

Transcript

00:01 So once again, welcome to a new problem.

00:06 This time we have a can liver, and it's stretching across like that.

00:15 So there's a can liver stretching across like that.

00:21 And it so happens to be supported by two columns.

00:27 One column is on the left edge, and then the other column is, somewhere right in the middle like that and the first column we call it a and then the second column we're going to call it b also it so happens that the first column supports the cunning lever with a force f a and then the second column also supports the kind of liver with a force fb and then in between these two columns, there's a gap or distance of 20 meters.

01:13 And then between the edge of the kind of the kind of liver and the second column, which is fb, we have a distance of 30 meters.

01:30 You know, that's the distance.

01:31 It so happens that the weight of the, or rather that the mass of the canal liver is given us is given us 1 ,000 so the mass of the canilever is given us 1 ,200 kilograms 1 ,200 kilograms the distance between the center of gravity of the kind of liver and the edge of itself is 25 meters that's the distance and also the gap between column b and the center of mass or center of gravity is five meters.

02:21 You know, that's the gap.

02:23 So this is the information that we've given in the problem.

02:26 And in this case, our goal is to find the two forces, f .a.

02:37 And fb that support the cunile liver.

02:42 That's our target.

02:44 Okay.

02:45 So, you know, we know there is equilibrium.

02:49 And the reason why we know there is equilibrium is because the the cunning liver doesn't collapse.

03:00 And because there is equilibrium, it means the two conditions are met.

03:04 You know, first of all, the sum of forces in the wide direction is zero and then the sum of the talks around any point whether it's a or b okay so some of talks around a zero and also some of the talks around b is also zero and those are the moments so we'll start by taking moments about a so we're assuming if the sum of the talks about a zero it means that the moments, the moments, we're focusing on the moments about a.

03:50 You know, these are going to be the moments about a.

03:53 A itself is right here.

03:56 And if you're taking moments, all the moments that are clockwise.

04:04 So all the, you know, we have the counterclockwise moment.

04:12 And then we also have the clockwise moments.

04:18 So there are two types, counterclockwise and clockwise.

04:23 I mean, assuming that the moments around a, the counterclockwise around a are positive, and then the clockwise moments around a are negative...

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