conical pendulum (easy type) (1 Viewer)

[dawso]

ok everyone, this is a pretty basic conical question but i swear the answer that the book has is wrong....giv us a hand

"if the number of revolutions per minute of a conical pendulum is increased from 75 to 100 find the rise in the level of the bob?"

 

[chubbaraff]

And we dont get the length of the string?
Raff

 

[robbo_145]

i get (7g)/(100pi)
where g is gravity

 

[Stefano]

"if the number of revolutions per minute of a conical pendulum is increased from 75 to 100 find the rise in the level of the bob?"

Hmmm.. seems tricky. I'll give it a go and let me know what you think.

When RPM=75;

75rpm=75pi/30 rad/sec

Now, v^2=rgtan@ & v=r[omega] (Equating and simplifying...)

tan@ = r[omega]/g = 75/30 {pi.r.[omega]/g}

When RPM=100;
100rpm=100pi/30 rad/sec

Using the same method we arrive at:

tan@ = 100/30 {pi.r.[omega]/g}



Thus, difference is [(100-75)/30] = 1/2 rad/sec

LOL this seems wrong...?

 

[~ ReNcH ~]

Is this a question from Fitz? If it is, then I think the answer is correct.

 

[Stefano]

Can anyone confirm my working correct/incorrect ??

How did you and Robbo get that answer anyways ?

 

[robbo_145]

Tcos@ = mg
Tsin@ = mrw^2

but from the basic diagram r = l sin@

therefore
Tcos@ = mg
T = mlw^2
divide the 2
cos@ = g/(lw^2)
lcos@ = g/w^2

but again from the basic diagram h = l cos@
thus
h = g/w^2 //(A)

now remember w = 2fπ where f is the frequency
thus for 75 revolutions /minute
w = (150π )/60 //converting to seconds
= 5π/2 rad/sec

for 100 revolutions /minute
w = 10π/3

plugging these values into (A) and finding the difference gives
4g/25π^2 - 9g/100π^2 = 7g/100π^2

woops its actually π^2 - hehe love the silly mistakes

 

[Ogden_Nash]

Hmm, I got the same answer as robbo, except with a pi² in the denominator...

Ah well robbo, that's 119/120

 

[~ ReNcH ~]

Suppose the particle describes a circle with radius "r" and the vertical height of the particle below the origin is "h".

Tsin@ = mrw²
Tcos@ = mg

.'. tan@ = rw²/g
but tan@ = r/h
.'. h = g/w²

w₁ = 75 revs/min = 5pi/2 rad/s
w₂ = 100 revs/min = 10pi/3 rad/s

.'. h₁ = 4g/25pi² and h₂ = 9g/100pi²

Difference in the height of the bob = h₁ - h₂ = 7g/100pi² as is in the answers in Fitzpatrick.

 

[dawso]

And we dont get the length of the string?
Raff

nah, no length..... (btw...are u raff as in eggs and rice capitan? )

also, no this question aint from fitzpatrick, i got it from "j Komaroni's circular motion" book....

but now that i look at fitzpatrick...i see the bitch stole this question from the other book i have....

and thanks 2 everyone else....the original book has one error in the working but looking through to his final answer.....its the same

cheers

-dawso

 

[chubbaraff]

Lol that would be me..... this is a latest... i get found out everywhere... but never in a forum... i take it your from the gong, smiths hill perhaps... coz like there the only 4u ppl i remotely associate with i think ...

 

[Vampire]

lol u prolly know joe then...

 

[dawso]

yeah raff, me and vampire at smiths hill boys, Greecke is also on here and pravski.....thats all i can think of for now....i actually met u at an 18th bout a month ago...small world aye

 

[chubbaraff]

pretty small, whose 18th?
Raff

 

[dawso]

....i beleive it was emmas.....i dunno, greecke just dragged me along and said it was a catholic school girls 18th.....i asked no more

 

[chubbaraff]

lol yeh jo used to go to our school... pretty bright kid ay
Raff

 

[dawso]

lol yeh jo used to go to our school... pretty bright kid ay
Raff

u say bright.....al i remeber is that i beat him in 3unit

 

[chubbaraff]

Wow... so Your Dawso... (the red nut... ) and greecke is Nick all the letters of the alphabet?

 

[chubbaraff]

lol i was soo drunk.. did i say indecent things about a certain girl?

 

[dawso]

lol i was soo drunk.. did i say indecent things about a certain girl?

.....i dont remember that much