Simplify this expression for the period

AI Thread Summary
The discussion revolves around simplifying the expression T = 2πLsinθ / √(Lgsinθtanθ). The user initially struggles with the simplification process despite reviewing their math notes. A suggestion to square the denominator and incorporate it into the radical leads to a successful simplification. The user expresses gratitude for the help and inquires about the rule used in the simplification. The response clarifies that this technique is known as "taking the square root" or "squaring."
crememars
Messages
15
Reaction score
2
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
 

Attachments

  • Screen Shot 2022-10-12 at 4.43.27 PM.png
    Screen Shot 2022-10-12 at 4.43.27 PM.png
    6.7 KB · Views: 127
Physics news on Phys.org
Hi,

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

##\ ##
 
If you square the denominator, you can put it inside the radical. What do you get?
 
kuruman said:
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
 
crememars said:
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.
$$\sqrt{\frac{A}{B^2}}=\frac{\sqrt{A}}{\sqrt{B^2}}=\frac{\sqrt{A}}{B}$$
 
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Struggling to make relation between elastic force and height'
Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
Back
Top