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$\bullet$ Chin brace. A person with an injured jaw has a brace below his chin. The brace is held in place by two cables directed at $65^{\circ}$ above the horizontal. (See Figure $1.23 . )$ The cables produce forces of equal magnitude having a vertical resultant of 2.25 $\mathrm{N}$ upward. (a) Make a scale drawing showing both the forces produced by the cables and the resultant force. Estimate the angle carefully or measure it with a protractor. (b) Use your scale drawing to estimate the magnitude of theforce due to each cable.

a) see drawingb) 1.241 $\mathrm{N}$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

University of Winnipeg

Lectures

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A $50-$ lb weight is hung …

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Cable $A C$ is $70 \mathrm…

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Two forces of $50 \mathrm{…

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this's Chapter one problem. 38. So it asks for a scale drawing showing both of these cable forces and the resultant force. So the result in force is going to be what happens when you add those two forces. Now it's nice to add forces by putting the vectors in tip to tail form, and that's what's going on in this diagram here. So these red lines are going along. The two, the two original cable forces, this one on the bottom is drawn just as it is in the diagram. And this one on the top with two red lines now is has just been translated. But without changing its length or its direction from its original position. Now you can add them to get this one in green. This is the result. Enforce the Net force and it should be going straight vertically straight up because we'll each of the cable forces have an accident. Why component the ex components? The horizontal components are going to be equal opposite, so they'll cancel out when you die. Directors together now, in part B, you want it wants you to use this drawing to estimate the magnitude of the force duty each cable. So we know that the lengths of vectors that you draw are proportional to their magnitude. Whatever units the magnitude may be in, we also know here the result in force has a magnitude of two 0.25 Newtons. So what you can do on your own diagram is measure the length of this vector. Let's call it l said our for l resultant. And then you can measure the length of one of the cable vectors Lets say L c for l table. And we know the ratios of the actual lengths should be the same as the ratios of the vector magnitudes. So l see. Over L R. Which you can measure is going to be equal tio the man tube of Force one or forced to, which should be equal, divided by the 2.25 mutants. And if you've done your diagram well, you've measured that 65 degree angle, which, and to be clear, this here is the 65 degrees. Then, in this equation, upon the top left you Khun, multiply both sides by 2.25 mutants Put in your numbers for Elsie and L R and you find that if one is going to be about F one is equal to have two, and they're gonna be about 1.24 And so that is the force that has asked for the force in either one of those two tables.

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