(II) Calculate FA and FB for the uniform cantilever shown in Fig. 7 whose mass is 1200 kg .

Name: Problem 9, Chapter 12: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2019-08-10T18:00:25-08:00
Duration: 3 min 7 s
Channel: Averell Hause
Description: (II) Calculate FA and FB for the uniform cantilever shown in Fig. 7 whose mass is 1200 kg .

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

Key Concepts

Static Equilibrium

Static equilibrium is a fundamental concept in mechanics where the sum of all forces and the sum of all moments (torques) acting on a body are zero. This principle is used to analyze structures to ensure that they are stable and not undergoing acceleration. It provides the basis for setting up equilibrium equations to solve for unknown forces in structures such as beams and frames.

Cantilever Beam

A cantilever beam is a structural element that is fixed at one end and free at the other. This type of beam is commonly used in engineering and architecture, and its analysis involves understanding how loads applied to the beam cause bending moments and shear forces. Its unique support condition requires special attention when calculating reaction forces and designing for stability.

Distributed Load and Uniform Mass Distribution

Distributed loading refers to a load applied over the entire length or area of a structure rather than at a single point. When a structure has a uniform mass distribution, the weight of the beam is spread evenly along its length. This concept is crucial when calculating the total load acting on the structure and determining the location of the load's resultant, typically at the centroid of the distribution.

Reaction Forces and Moment Calculations

Reaction forces are the forces provided by supports or connections that balance the applied loads in a structure. In the context of a cantilever beam, calculating these forces involves taking moments about a chosen point and applying the conditions of static equilibrium. Moment calculations are essential to determine how far from the fixed support the equivalent force acts, ensuring that both force and moment balance equations can be effectively applied.

Weight and Mass Conversion

In dynamics and static analysis, mass must be converted into weight when gravitational forces are involved. This is done by multiplying the mass by the acceleration due to gravity. Understanding this conversion is essential when analyzing the influence of a uniformly distributed load due to the beam’s own weight, particularly when dealing with reaction forces and moments in the structure.

Transcript

00:01 Here's the diagram of the system and we know that the system has static equilibrium as well as translational equilibrium in the y direction.

00:07 So we can apply the sum of torques.

00:09 This will equal 0 and this would equal 4 sub b multiplied by 20 .0 meters minus m g multiplied by 25 .0 meters.

00:24 This is equaling 0 and so we can say that the force sub b would be equaling 25 .0.

00:31 Divided by 20 .0 multiplied by m .g.

00:37 This is equaling 1 .25, multiplied by 1 ,200 kilograms, multiplied by 9 .80 meters per second squared.

00:50 And so we find that the magnitude of force sub b is equaling 1 .5 times 10 to the 4th newton's.

00:59 We are getting a positive answer, which means that this indeed, points upwards.

01:05 If we're with hypothetically we were getting a negative answer, that means that the direction that we had expressed f sub b in the diagram would be the opposite and this would actually be pointing downwards if we were if this was a negative answer.

01:22 But here we obtained a positive answer so how we represented force sub b in the diagram is correct and it is indeed upwards.

01:30 Now we're going to apply the sum of forces.

01:33 In the the y direction, this would be f sub a plus f sub b minus mg.

01:40 This is equaling zero.

01:42 And so we can say that f sub a is equaling mg minus f sub b...

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