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Old 01-21-2012, 05:34 PM   #62
Join Date: Aug 2011
Posts: 335

Originally Posted by Koz View Post
You pick Cos or Sin depending on what angle you know (or what angle you want to use). In the original post we use cos because the angle we measure is the angle Q, which is the angle between the horizontal direction and the arm. Cos gives the correct properties for this setup. It has a max value (1) at zero degrees (when the bar is horizontal), and a minimum value (0) at 90 degrees (when the bar is vertical). In comparison sin has a max value at 90 degrees. So if we used Sin in the equation we'd be saying you get max tension when the weight arm is pointing straight up or straight down! We know this isn't true, because if you're really good at balancing, you could balance the weight arm vertically without ANY tension on the string! You definitely can't hold the arm horizontal without tension on the string though!

However, you could also look at the problem from a different direction. If you defined the angle Z as the angle between the lever arm and the vertical direction (instead of the horizontal direction), your tension would be max when Z=90 degrees. Z=90 degrees is the same position as Q=0 degrees.

The original tension equation in the 1st post was:
f = (M g / r) (cos Q) R

If you use Z instead of Q you'd just get:
f = (M g / r) (sin Z) R

Note that the physics didn't change at all, you just looked at it differently the 2nd time. So you pick Sin or Cos depending on how you look at the problem.

It's good you ask the question here, because if you can make sense of this now it will be really helpful for you in your AP class. A lot of times you'll learn an equation one way (with sin), but you'll be given a problem where the angle you're given means you need to use Cos instead. Try to do a quick "does this make sense" check when looking at these problems. Ask yourself "what happens when the angle is zero?" or "what happens when the angle is 90?" If the value is biggest at zero, you know to use cos. If it's biggest at 90, you know to use sin.

So in this case, you ask "what happens when Q is zero?" well the bar is horizontal and you get your max tension. Which trig function is maxed at zero? Cos.

If you asked "what happens when Q is 90?" you'd have to think about it...if Q is 90 then the bar would be standing up vertically. If you had it perfectly balanced so that it was standing up all by itself, how much tension would you have to apply to keep it vertical? Zero lbs! In other words, your tension is a minimum (zero) when the arm is vertical. What trig function is a minimum at zero? Cos. So you use Cos for this problem when given angle Q.

Note, if you are dead set on using sin in your equation, you still can't use Sin(Q), but you can use Sin(90-Q), since that's the same thing as Cos (Q). It's just whatever way you're most comfortable with, or what makes the most sense to you.
I got it. Thanks for the response. My teacher wants it to be perpendicular to the force, so i was a little confused. It makes perfect sense.
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