pendulum swing --basic trig problems 1. The problem statement, all variables and given/known data lets say you have a pendulum swinging. the length of string is 1m it swings to the right so that the angle is 45deg. i want to find difference in height from when it is at rest to its new position at 45deg. How do i do this, trigonomically speaking i mean? i mean, where is the right triangle??? 2. Relevant equations not exactly a homework prob, but related to everything in homework 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution i think i forgot sum basic trig, cause i cant figure out where the right angle triangle is to get my lengths from/????
The string of the pendulum is the hypoteneuse. Draw a vertical line through the top of the pendulum (like when the pendulum is at rest)... now draw a horizontal line from the swinging end of the pendulum to this vertical line. do you see the right triangle now?
book says to go something like L-Lcos45 = L(1-cos45) i dont undetsand why they say that, because when i apply basic trig (cos45 = adj/hyp) i get a totally differnt number than book ??
Yes. The hypoteneuse is always 1m. But the vertical line changes length. You can calculate the length of the vertical using the hypoteneuse and the angle.
They're taking the difference. Originally the length of the vertical is L... then later the length of the vertical is Lcos45. So the difference in height is L - Lcos 45
I'm not sure what you mean by cuts off the hypoteneuse... the pendulum is always the same length... and the string of the pendulum forms the hypoteneuse...
At the 45 degrees position, the hypothenuse is no longer vertical!! The hypothenuse is along the string and is 1 meter long. The two other sides (horizontal and vertical) are of course smaller than 1 meter. they are of course L sin45 and L cos 45, respectively. Ithink that you are still drawing the position of the string when it is at zero degree and this creates confusion. It might be better to draw on a separate figure, next to the first one, the position of the string when the object is at the lowets position. It should be clear that the difference of height is L - L cos 45.
The hypoteneuse has length L... the adjacent is the vertical. adj/hypoteneuse = cos 45 adj/L = cos 45 adj = Lcos 45