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Home Q & A Board Science-Related Homework Help Physics
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Anonymous galacxie
wrote...
A year ago
Determine the cables' tensions, normal force in the smooth surfaces, and the angle of inclination of the surface on the right if the block on the left and right weighs 150N and 200N, respectively.

I sort of understand how to get the answer, but determining the second angle is stumping me.
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#1
Educator
A year ago
Hello, I think the angle is 42.2 degrees.

Is that what you found for theta?

My work is shown below!
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Anonymous Author
wrote...
#2
A year ago Edited: A year ago
Quote from: bio_man (A year ago)
Hello, I think the angle is 42.2 degrees.

Is that what you found for theta?

My work is shown below!

OP here, I actually played around with the acceleration equation assuming a=0 to derive the second angle, which I guess is wrong because I got 33.6  Grinning Face with Smiling Eyes
I used this formula: \(A=\frac{w_2\sin θ-w_1\sin θ}{m_1+m_2}\) where w1=150, w2=200, m1=150/9.81, m2=200/9.81

I haven't had a physics class in a while haha.
wrote...
#3
Educator
A year ago
Can you elaborate on how you got 33.6°?
Anonymous Author
wrote...
#4
A year ago
Quote from: bio_man (A year ago)
Can you elaborate on how you got 33.6°?

So I used a=fm into this equation: \(a=\frac{w2sinθ−w1sinθ}{m1+m2}\)
substituting the values I got: \(a=\frac{200sinθ−150sin30}{150/9.81+200/9.81}\)
Assuming a=0 since it is at rest, I derived the angle from the equation hence 33.6 degrees.

Btw, can I ask where did sqrt 2 and \(θ-\frac{\pi }{4}\) come from in the last part of your solution?
wrote...
#5
Educator
A year ago Edited: A year ago, bio_man
I used trigonometric identities to derive that. I can't recall all the steps I took, but I did use the Pythagorean identity along with several others. You can verify it works by placing some random theta into both, and they'll equal the same output.
Anonymous Author
wrote...
#6
A year ago
Quote from: bio_man (A year ago)
I used trigonometric identities to derive that. I can't recall all the steps I took, but I did use the Pythagorean identity along with several others. You can verify it works by placing some random theta into both, and they'll equal the same output.

I see, thank you very much for your help!
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