Pendulum swing -basic trig problems

[mujadeo]

pendulum swing --basic trig problems

Homework Statement

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?

Homework Equations

not exactly a homework prob, but related to everything in homework

The Attempt at a Solution

i think i forgot sum basic trig, cause i can't figure out where the right angle triangle is to get my lengths from/?

 

[learningphysics]

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?

 

[mujadeo]

but if i do that, then vertical line is no longer 1m??

 

[mujadeo]

because when it swings it is higher than it was at rest

 

[mujadeo]

book says to go something like L-Lcos45 = L(1-cos45)
i don't undetsand why they say that, because when i apply basic trig (cos45 = adj/hyp) i get a totally differnt number than book

??

 

[learningphysics]

because when it swings it is higher than it was at rest

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.

 

[mujadeo]

so even though the right triangle cuts off the hypotenuse, i should still use hyp as 1m

 

[learningphysics]

book says to go something like L-Lcos45 = L(1-cos45)
i don't undetsand why they say that, because when i apply basic trig (cos45 = adj/hyp) i get a totally differnt number than book

??

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

 

[mujadeo]

pleae allow the dumb question
--what is Lcos45 derive from?
i can't match it up to SOHCAHTOA?

 

[learningphysics]

so even though the right triangle cuts off the hypotenuse, i should still use hyp as 1m

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...

 

[nrqed]

so even though the right triangle cuts off the hypotenuse, i should still use hyp as 1m

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.

 

[learningphysics]

pleae allow the dumb question
--what is Lcos45 derive from?
i can't match it up to SOHCAHTOA?

The hypoteneuse has length L... the adjacent is the vertical.

adj/hypoteneuse = cos 45

adj/L = cos 45

adj = Lcos 45

 

[mujadeo]

thanks you
understand now