Questions and Problems (1) Use head-to-tail graphical vector...

Questions and Problems (1) Use head-to-tail graphical vector addition to find \(\vec{R}\) and then \(\vec{E}\) in Procedure 1. Show your graph below, using a scale of 0.4 N = 1 cm. Use a ruler and a protractor to carefully construct the vectors \(\vec{F_1}\) and \(\vec{F_2}\) from their measured values, and apply direct measurement on your graph rather than trig or geometry to find \(\vec{E}\). Finally, compare your theoretical prediction for \(\vec{R}\) from this graph to the measured values obtained previously in Procedure 1 Procedure 1 Graph Scale 0.4 N = 1 cm \(\vec{E}\) Theoretical Experimental % Difference Prediction Measurement Mass .2817kg .2816kg .39% Force Magnitude 2.77N 2.76N .36% Angle 286.6° 286.5° .035%

Transcript

00:01 In this video, i'm going to be working with vector addition.

00:03 Okay, we're given two vectors, two force vectors, and we want to add them together.

00:07 We're going to be doing this in three ways.

00:09 We're going to be doing it mathematically first, so we're going to be breaking down the vectors into their x and y components and adding them that way.

00:16 Then we're going to do this addition graphically by hand, and for that we'll need a piece of graph paper, a protractor, and a ruler.

00:24 The last way i'm going to do it is to use a graphing software.

00:28 And once i've done those, once i've found the sum three ways, i'm going to compare them and see how they compare.

00:34 Okay, so let's look at our problem statement.

00:37 We have two ropes that are pulling on a log.

00:40 Okay, so we have two forces from the ropes.

00:43 Okay, force one has a magnitude of 12 newtons.

00:48 Okay, and that's at an angle theta 1 of 10 degrees.

00:53 Okay, with respect to the horizontal axis.

00:56 Okay, so say the line.

00:57 Logs at the origin.

00:59 This is a horizontal and the vertical axis.

01:03 Okay, so my theta one's going to be somewhere over here.

01:06 Okay, my second force vector has a magnitude of eight newtons.

01:13 Okay, and that's at an angle theta two of 120 degrees with respect to the same axis.

01:20 Okay, so that's going to be somewhere up there.

01:22 Okay, so let's break down these vectors.

01:24 Okay, force one equals 12.

01:29 Nukes times cosine of 10 degrees x plus sign 10 degrees y that's in newtons okay so that equals 11 .1 .8 newtons x plus 2 .08 8 newtons y my second vector f2.

02:04 Equals 8 newtons times cosine 120x plus sine 120y y.

02:20 Okay, in newtons.

02:23 And that gives me negative 4 newtons x plus 6 .93 newtons y.

02:34 And we want to find the sum of these.

02:36 Okay, so i'm going to call that f sub r for result.

02:38 Equals f1 plus f2 okay and that gives me 7 .8 newtons x okay plus 9 .01 newtons y so this is my result in vector and component form okay we want to find the magnitude and direction okay so the total magnitude of the vector and then the angle that it makes with the horizontal axis okay so to find the magnitude f sub r that equals the square root of f sub r x squared plus f sub r y squared okay that gives me a magnitude of 11 .9 mutants and let's find that angle i know that the tangent of theta r equals my y component over my x component, so fyr over f xr.

03:45 Okay, so from that i get theta, oops, theta r equals 49 degrees with respect to the horizontal.

03:59 Okay, so we have a magnitude of 11 .9 and an angle of 49 degrees.

04:06 Okay, next let's look at it graphically.

04:08 Obviously, i can't draw on a piece of paper, but i can use this coordinate grid...

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