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Question Number 218030 by Tawa11 last updated on 26/Mar/25

Commented by mr W last updated on 26/Mar/25

$t h e m a n y w a t e r m a r k s a r e t e r r i b l e!$
Commented by mr W last updated on 26/Mar/25

$s e e Q 216110$
Commented by Tawa11 last updated on 26/Mar/25

$Done sir .$ $Thanks sir .$ $I appreciate .$
Commented by mr W last updated on 26/Mar/25

$w h a t d i d y o u g e t ∣ B C ∣= ?$
Commented by Tawa11 last updated on 26/Mar/25

$0 . 4 m sir$
	Answered by mr W last updated on 02/Apr/25

	Commented by Tawa11 last updated on 02/Apr/25

	$Thanks sir .$ $I appreciate .$
	Commented by mr W last updated on 02/Apr/25

	$l_{0} = 1.2 m$ $λ = 40 N$ $k = \frac{λ}{l_{0}} = \frac{40}{1.2} = \frac{100}{3} N / m$ $a t p o i n t A :$ $l_{1} = 4 m$ $Δ l_{1} = 4 - 1.2 = 2.8 m$ ${P E}_{1} = \frac{k Δ l_{1}^{2}}{2}$ $a t p o i n t B :$ $l_{2} = 2 m$ $Δ l_{2} = 2 - 1.2 = 0.8 m$ ${P E}_{2} = \frac{k Δ l_{2}^{2}}{2}$ $f r o m A t o B :$ $d i s t a n c e m o v e d : l_{1} + l_{2} = 6 m$ $f r i c t i o n f o r c e f = μ m g$ $f (l_{1} + l_{2}) = \frac{k (Δ l_{1}^{2} - Δ l_{2}^{2})}{2}$ $\Rightarrow f = \frac{k (Δ l_{1}^{2} - Δ l_{2}^{2})}{2 (l_{1} + l_{2})}$ $= \frac{100 (2 . 8^{2} - 0 . 8^{2})}{3 \times 2 \times 6} = 20 N$ $o r$ $μ = \frac{f}{m g} = \frac{20}{7 \times 9.81} \approx 0.291$ $a t p o i n t B :$ $t e n s i o n i n s t r i n g :$ $T_{2} = k Δ l_{2} = \frac{100 \times 0.8}{3} = 26.67 N > f$ $\Rightarrow p a r t i c l e w i l l m o v e t o w a r d s l e f t .$ $s a y ∣ O C ∣= 1.2 + x w i t h 0 < x < 0.8,$ $i . e . ∣ B C ∣= 0.8 - x$ $Δ l_{3} = x$ ${P E}_{3} = \frac{{k x}^{2}}{2}$ $\frac{k (Δ l_{2}^{2} - x^{2})}{2} = f (0.8 - x)$ $\frac{100 (0 . 8^{2} - x^{2})}{3 \times 2} = 20 (0.8 - x)$ $5 x^{2} - 6 x + 1.6 = 0$ $\Rightarrow x = \frac{3 - \sqrt{9 - 5 \times 1.6}}{5} = 0.4 m$ $\Rightarrow∣ B C ∣= 0.8 - 0.4 = 0.4 m$ $T_{3} = k x = \frac{100 \times 0.4}{3} \approx 13.3 N < f = 20 N$ $a t p o i n t C p a r t i c l e {d o e s n}^{'} t m o v e$ $f u r t h e r .$
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