Finding Equilibrium Force: Is it Correct?

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The discussion focuses on calculating the equilibrium force using trigonometric principles. The angle was determined using the tangent function, leading to a calculation of the hypotenuse force, which resulted in approximately 3010.4 N. The calculations are deemed correct, considering the significant figures provided in the problem. The conversation highlights the concept of mechanical advantage, explaining how applying a smaller force at a larger angle can yield a significantly larger resultant force. This demonstrates the principles of force application in mechanical systems effectively.
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the question is http://home.earthlink.net/~urban-xrisis/clip_image002.jpg

so first I found the angle...
tan\theta=\frac{O}{A}=\frac{0.5}{6}
\theta=4.7636416

I then needed to find the force of the hypotnuse...
sin\theta=\frac{O}{H}
H=\frac{250N}{sin4.7636416}

H=3010.3987N

is this correct?
 
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I didn't bother going through your work, but I got the same answer, 3010.4 N. So I assume it's correct. Also, the distances in your problem were given to 2 significant digits, so realistically the answer is correct to only 2 sig dig.
 
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That looks good to me. Assuming all of your calculations are correct, that seems to be the correct method for solving this problem.
 
it just seems amazing that if you applied only 500 Newtons, you will get a resultant force of over 6 times of what you applied.

how can that be?
 
Mechanical advantage. You are applying force against a much larger angle than the force applied against the car. The difference in this angle will result in the force on the car being much greater.
 

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