(II) Redo Example 9-9, assuming now that the person is less bent over so that the 30^∘ in Fig. 9

(II) Redo Example 9-9, assuming now that the person is less...

Key Concepts

Trigonometric Analysis

The use of trigonometric functions like sine and cosine is essential for relating the angles of applied forces to their components. Adjusting the bending angle, such as switching from 30° to 45°, changes these components, which directly influences the calculation of forces exerted on the spinal structures.

Static Equilibrium

This concept involves analyzing a system where all forces and moments balance so that there is no net motion. In biomechanical applications, such as calculating forces on the vertebrae, static equilibrium is used to determine how forces are transmitted and balanced in the body during different postures.

Force Decomposition

Force decomposition involves breaking a force into its component parts along specified directions, typically using trigonometric functions. This is key in biomechanics when calculating the individual contributions to spinal loading, as forces acting at an angle must be resolved into vertical and horizontal components to understand their effects.

Torque and Moment Arms

Torque, or moment, is produced by a force acting at a distance from a pivot point. In the context of spinal biomechanics, changing the angle of bending alters the effective moment arm of the applied forces, thereby affecting the magnitude of the resultant load on the vertebrae.

Transcript

00:01 All right, so chapter 9, problem 33, redo example of 9 -9, assuming now that the person is less spent over, so that the 30 degrees in figure 9 -14b is instead 45 degrees, what will be the magnitude of fb on the vertebra? so the vertebra are depicted here in the b picture, and here are both figures b and c if you don't have them with you.

00:29 At least here are free body diagrams with them and so this is figures i would say figure c is more like a kind of a blown up picture right there so we have fm right then we have the angles around fm so you have 33 degrees above we'll below the horizontal and then a little 12 more degrees downwards we have a separate area so there's a lot of stuff we want to go over here but let's just kind of go through real quick so we're still going to assume that the back muscles pull at a 12 degrees to the spine the distances haven't changed in between anything oh sorry this is 45 one to 30 but it actually is the other way around my bad 30 goes to 40 but 18 does go to 33 that's true so yeah this this used to be 18 in the previous problem in the example but now it's at 33 so there's a couple things different and then we can just say we can use these free body diagrams or we can use these force diagrams to uh to find this fv based on all the other stuff that we are given so we want to take the base of the spine as the pivot and as usual we will take counterclockwise torques as positive so this means that this kind of torque is going to be positive, this kind of torque is going to be negative, and so we can go ahead and begin with our calculation here.

02:30 So here's the sum of the torques equal to zero, and we have a lot of terms.

02:38 So as in the original, let's just go to the bottom real quick.

02:40 Wh is 0 .07, w .a is 0 .12 and w .t, sorry, is.

02:48 Is 0 .46w.

02:51 These are all attached with their distances here.

02:54 And so these distances haven't changed from the previous problem.

02:58 0 .48, 0 .72, and 0 .36, all with that same sign and angle.

03:10 And then we also have to consider the 12 degree part.

03:15 So yeah.

03:18 If we imagine that we have the base of the spine as a pivot, that means it'll be right here.

03:25 This will be our pivot point.

03:27 So this can kind of give you an idea why we have certain terms as positive and negative.

03:31 So anything following this error is going to be positive.

03:34 Anything going against the arrow is going to be negative.

03:40 With that, we can just add up the terms very easily.

03:43 So let's go to the next page here, or it's a little bit more simplified.

03:50 So i just took the liberty to put fm on its side, on the left side, and then everything else on the right side.

03:59 I also factored out w here, so you'll see that here at the back, and then sign 45 as well.

04:06 It's also factored since all the terms on the top had it.

04:11 But yeah, this ends up just being a number...

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