Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of

Due to a jaw injury, a patient must wear a strap (Fig. E4.3)...

Key Concepts

Static Equilibrium

Static equilibrium is the condition in which an object remains at rest or moves with constant velocity because the net force and net torque acting on it are zero. This concept is crucial in evaluating setups like the strap scenario, where the forces must balance to provide the required net force in the desired direction.

Tension

Tension is the force transmitted along a flexible connector such as a rope, cable, or strap when it is pulled tight by forces acting from its ends. It acts uniformly along the length of an ideal, massless connector and is a fundamental concept in analyzing forces in systems in equilibrium.

Force Components

Force components refer to the process of breaking down a force vector into perpendicular parts, usually along axes such as horizontal and vertical. This is essential in problems where forces act at angles, as it allows for the application of trigonometric methods to determine the contribution of each component to the overall net force.

Transcript

00:04 Okay, so this is another two -dimensional vector decomposition problem, and i will try my best to redraw the diagram, the figure that's given the textbook, e4 .3.

00:19 So basically what's going on is that we have a patient wearing a chin strap.

00:28 It looks a little something like this.

00:31 So it's pulling on him in these two diagonal directions, and then it catches up to these little wheels.

00:40 Come back around and make kind of a diamond shape.

00:45 And they meet back in the center, they're pulling upwards.

00:47 So again, there's a little rotational wheel here, and another rotational wheel here.

00:52 And then a key, a piece of information that's only given in the figure is that the angle in between these two straps is the angle theta, which is 75 .0 degrees.

01:09 And this problem will need that number in order to numerically solve the problem.

01:16 That's 75 .0 degrees.

01:19 Okay, so that's great.

01:20 We have an upward the force and an upward right force.

01:24 And then really importantly is that we're not actually going to be using the angle theta.

01:28 So which is the angle theta over 2 in this problem because there's a line of symmetry going down the bottom.

01:35 So let's use the head -to -tail method for vectors in order to put them from head -to -tail.

01:44 So let's do the left vector first and then the right vector second.

01:48 So we know that it's metrics, so they're going to be the same magnitude.

01:56 And then they'll, if we do it like this, they will end up with a perfectly straight at vector.

02:00 Let's call that f tote.

02:06 And then again, they're two equal and opposite.

02:10 Sorry, they're two equal, but not opposite vectors.

02:15 So we'll call them t for tension.

02:17 One in the upward left direction and the other one in the upward right direction.

02:22 Their angle theta over two is sneakly hiding over here in this corner.

02:28 As well as this upper corner.

02:35 So we have another natural line of symmetry, and that is the horizontal, and going right here, to show that we have a nice right angle between the horizontal axis, and our f -toed vectors, so now would be a good time to define a coordinate system, that being x in the horizontal direction, just a classic coordinate system, and then y, going upward in that vertical direction.

02:59 So let's start translating free body diagrams.

03:02 Into actual equations...

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