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$\cdot$ On a single diagram, carefully sketch each force vector to scale and identify its magnitude and direction on your drawing: (a) 60 lb at $25^{\circ}$ east of north. (b) 40 lb at $\pi / 3$ south of west.(c) 100 lb at $40^{\circ}$ north of west. (d) 50 lb at $\pi / 6$ east of south.

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Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

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Calculate the resultant fo…

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The magnitudes and directi…

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Vector $\vec{a}$ has a mag…

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Find (a) "north cross…

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The vectors a and b repres…

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If a vector $\vec{A}$ has …

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03:57

Draw each of the following…

this's Chapter one problem. 34. In this problem, we're given the magnitude and directions of four different vectors, and we are asked to draw them carefully on a diagram. Now, since I am working on a virtual whiteboard, I'm going to draw them not so carefully. What I recommend you do at home is get out Penner pencil paper and a protractor and a ruler. The protractor is forgetting your angles directly. The ruler is both for drawing directors in a straight line and forgetting the length of directors all on the same scale. Now the vectors are in units of pounds. Obviously, pound is not a unit of length, but so we only she was pick a scale where on actual unit of length on your paper is equivalent to some number of pounds. I would suggest something like one centimetre is equal to 10 pounds, because then the four vectors you're given are going to be six centimeters, four centimeters, 10 centimetres and five centimetres long, which are nice round numbers in the kind of thing that will fit well on a sheet of paper. So let's get started. Vector A. We're told it's 60 pounds a 25 degrees east of north, so it's put in our compass directions. That's north, east, south and west, so our angle is given at east of North. That means we're going to measure it from the north, access in this direction to the east. So we're going to get an angle of 25 degrees and then draw our vector. It's going to be smaller here, but I'd put you know six centimeters on your own paper or are a length. It's equivalent to 60 pounds, and that's a record, eh? Protector be is 40 pounds at Pi, over three south of west, so south of west, it's going to be measured in this direction from the West. Access the pie over three is measured in radiance, but if you're using a protracted, you could do this. You've probably got a Martian degrees, so let's convert those radiance in two degrees, and to do that, you multiply your radiance value. Buy 1 80 degrees divided by pi, and in this case, that's going to get us 60 degrees. So we need to measure a 60 degree angle in the direction of that red arrow from the West. Access and Victor's 40 pounds. So however long you drew the 60 pound doctor A. This one should be 2/3 as long, so roughly like this. And it's not. Note this, since this angle was 60 degrees. This vector B is 30 degrees from the south axis. Where's after is only 25 degrees from the north access. So they're close to parallel. But they are not quite parallel. They're not quite not. The directions after a should be a little more drawn, a little more vertical, a little more steeped in Dr B. Now a vector C is 100 pounds at 40 degrees north of west. So now we're measuring from the West access again. But in the north direction, we're giving our angle and degrees so we can just draw a vector at that angle. And it's 100 pounds, so it needs to be longer than everything else. Not quite not quite twice as long as after a and again doing this on your own. He should measure carefully links the vectors so that no, the ratio of the lengths a vector aid of sea is 6 to 10. Exactly. Finally, factor D. 50 pounds of pie over six east of south so east of south means we're measuring our angle from the south access to the east direction again. We're given it in radiance pie over six so we could convert like we did before, multiplied by 180 degrees over pie. Or we could just notice that pie over six is half a pie over three. So this angle should be half of 60 degrees, meaning that it is 30 degrees and so will draw it about 30 degrees. And this is 50 pounds or vector should be exactly half as long as vector. See on that's your after tea and there you go. See, your drawing should look something like this, but neater and with all your angles and distances measured precisely.

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