here is a question really troubling me. A cylindrical tube rolling down a slope of inclination θ moves a distance L in the time T. The equation relating these quantities is L(3+(a^2 /P))=QT^2 sin θ where a is the internal radius of the tube and P and Q are constants.What are the units of P and Q?


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Question Number 31149 by NECx last updated on 03/Mar/18

$h e r e i s a q u e s t i o n r e a l l y t r o u b l i n g$ $m e .$ $A c y l i n d r i c a l t u b e r o l l i n g d o w n a$ $s l o p e o f i n c l i n a t i o n θ m o v e s a$ $d i s t a n c e L i n t h e t i m e T . T h e$ $e q u a t i o n r e l a t i n g t h e s e q u a n t i t i e s i s$ $L (3 + \frac{a^{2}}{P}) = {Q T}^{2} \sin θ w h e r e a i s$ $t h e i n t e r n a l r a d i u s o f t h e t u b e a n d$ $P a n d Q a r e c o n s t a n t s . W h a t a r e$ $t h e u n i t s o f P a n d Q ?$
Commented by NECx last updated on 03/Mar/18

$h e r e i s w h a t I d i d . . . . .$ $2 g h = v^{2} (1 + K^{2} / r^{2})$ $2 g L s i n θ = v^{2} (1 + k^{2} / r^{2})$ $v^{2} (1 + k^{2} / r^{2}) = 2 g L \sin θ$ $(\frac{L^{2}}{T^{2}}) (1 + k^{2} / r^{2}) = 2 g L s i n θ$ $L (1 + k^{2} / r^{2}) = 2 {g T}^{2} s i n θ . . . . . (1)$ $L (3 + a^{2} / P) = {Q T}^{2} \sin θ . . . . . . . (2)$ $∴ P = L^{2} a n d Q = g = {L T}^{- 2}$ $I r e a l l y h a v e a d o u b t o n t h i s p l e a s e$ $c h e c k a n d c o r r e c t . T h a n k s$
	Answered by mrW2 last updated on 03/Mar/18

	$I f y o u j u s t n e e d t o k n o w t h e u n i t s o f$ $P a n d Q, y o u {d o n}^{'} t n e e d t o$ $k n o w a l l t h e f o r m u l a, e v e n y o u {d o n}^{'} t$ $n e e d t o u n d e r s t a n d p h y s i c s .$ $\frac{a^{2}}{P} h a s t h e s a m e u n i t a s 3, s o P h a s$ $t h e s a m e u n i t a s a^{2}, i . e . [L^{2}] .$ $T h e u n i t o f l e f t s i d e i s [L], t h e r i g h t$ $s i d e m u s t a l s o h a v e t h i s u n i t .$ $s i n θ h a s n o u n i t .$ $T h a s t h e u n i t [T] .$ $\Rightarrow [Q] \times [T^{2}] = [L]$ $\Rightarrow [Q] = [\frac{L}{T^{2}}]$ $i . e . t h e u n i t o f Q i s [\frac{L}{T^{2}}], e . g . m / s^{2} .$
	Commented by NECx last updated on 03/Mar/18

	$o h . . . . T h a n k s$
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