Mechanics

- TrojanPoem

Mechanics

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- TrojanPoem

@phi

- Jack1

what specifically about mechanics? do u have an engineering based question?

- TrojanPoem

Nah, general question.

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## More answers

- TrojanPoem

Are you an engineer ?

- phi

|dw:1444139335225:dw|

- Jack1

nah, just ok at maths

- phi

if we use the Law of Cosines on that triangle
|dw:1444139454924:dw|

- TrojanPoem

That's why I was getting the wrong angles -,-

- phi

x is the angle between u and v
but in the triangle the "opposite angle" is 180 - x
cos (180-x) = - cos(x)

- phi

a picture drawn to scale is very helpful. (If done very accurately, you can measure the answer), but even a rough drawing gives a good estimate of the answer (i.e. angle and length of the vector)

- TrojanPoem

How ? It wasn't clear 131 ? on the last question

- phi

Using the Law of Cosines idea?
|dw:1444139889064:dw|

- TrojanPoem

|dw:1444139666557:dw|

- TrojanPoem

Why isn't 180 - Alpha = alpha ? Symmetry

- phi

alpha (apparently, based on the answer choices) is the angle between v and f
the angle between u and v is alpha + theta

- TrojanPoem

|dw:1444140291240:dw|

- phi

yes. with theta= 40, you get 120-alpha
now it will work

- phi

*140 - alpha

- TrojanPoem

300/ sin alpha = 256.9 / sin40
sinalpha^-1 = 48.64 -,-

- TrojanPoem

What am I doing wrong ?

- phi

I think it would help if you drew a picture that more closely matched the situation

- TrojanPoem

|dw:1444140790074:dw| That's our start then |dw:1444140826725:dw| then using the sine rule.

- phi

as you know the Law of Sines is ambiguous when you have an obtuse angle
notice sin(131.4)= sin(48.6)
In this problem, you have to recognize you should choose the 131.4

- phi

|dw:1444141166027:dw|

- phi

V almost doubles back on u, and we have an obtuse angle opposite the longest side = 300
Considering these subtleties, perhaps using components (of vectors) is more straightforward

- TrojanPoem

Using vectors'd give me the answer directly, however, I've to answer this question using cosine / sine rule :/

- phi

the other way around the ambiguity is choose the acute angle rather than alpha

- TrojanPoem

140 - alpha ?

- TrojanPoem

Alpha doesn't seem like an obtuse in the drawing :/

- phi

|dw:1444141658047:dw|

- TrojanPoem

Fine, thanks phi :)

- phi

\[ \frac{\sin (140-\alpha)}{60}= \frac{\sin(40)}{256.9}\]

- TrojanPoem

Phi, I noticed that 256.9 is out of the choices -,-

- TrojanPoem

a)112.7 b ) 145.9 c) 154.3 d ) 257.9

- TrojanPoem

@phi

- phi

Yes, I noticed that before. I assume it is a typo.
Here are the 3 vectors

##### 1 Attachment

- TrojanPoem

Ok, as you're sure.

- phi

You can ask your teacher, but the numbers work out to 256.9

- TrojanPoem

Yeah, 257.9 works too with 131.4

- TrojanPoem

u+v= f
so
v= f-u
f=<300,0> (we let f point along the x-axis
u= 60
v= <60 cos(40) - 300, -60 sin(40) >
now find the magnitude and angle of v
|v| = 256.9
angle = atan(y/x) = 8.6 deg in the 3rd quadrant= 171.4
alpha = 171.4-40= 131.4 deg
maybe it's a typo we've two solutions here which come with the same result.

- phi

Yes, I'm sure the magnitude is 256.9
But complain to your teacher.

- TrojanPoem

I will.

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