Simplify this expression for the period

  • Thread starter crememars
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  • #1
crememars
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Homework Statement:
A bob of mass m is suspended from a fixed point with a massless string of length L. You are to investigate the motion in which the string moves in a cone with half-angle, 𝜃. Express your answers in terms of some or all of the variables m, L, and 𝜃, and g.

v = √Lgsin𝜃tan𝜃

How long does it take the bob to make one full revolution (one complete trip around the circle)?
Relevant Equations:
T = 2πr / v
r = Lsin𝜃
hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my math notes too.

my expression for T is:

T = 2πLsinθ / √(Lgsinθtanθ)
T = 2πLsinθ * √(Lgsinθtanθ) / Lgsinθtanθ
T = 2π * √(Lgsinθtanθ) / gtanθ

final answer

[ 2π * √(Lgsinθtanθ) ] / gtanθ

the correct answer should be:

2π * √( Lcosθ / g )


thank you in advance
 

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Answers and Replies

  • #2
BvU
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Hi,

How about the forces that act on the bob ? Can you draw a diagram ?

##\ ##
 
  • #3
kuruman
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If you square the denominator, you can put it inside the radical. What do you get?
 
  • #4
crememars
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If you square the denominator, you can put it inside the radical. What do you get?
tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it
 
  • #5
kuruman
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tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it
It's called "taking the square root" or "squaring". You can go back and forth in what is shown below.
$$\sqrt{\frac{A}{B^2}}=\frac{\sqrt{A}}{\sqrt{B^2}}=\frac{\sqrt{A}}{B}$$
 

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