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Question Number 136930 by I want to learn more last updated on 27/Mar/21

Commented by I want to learn more last updated on 27/Mar/21

Commented by Olaf last updated on 28/Mar/21

$(i) W = \frac{1}{2} {K x}^{2}$ $K = \frac{2 W}{x^{2}} = \frac{2 \times 10}{0, 05^{2}} = 8000 N m^{- 1}$ $(i i) F = K x = 8000 \times 0, 05 = 400 N$ $(i i i) F = m a \Rightarrow a = \frac{F}{m} = \frac{400}{2} = 200 {m s}^{- 2}$ $(i v) V_{P} = a t = 200 \times 0, 25 = 50 {m s}^{- 1}$ $M_{P} V_{P} + M_{Q} V_{Q} = (M_{P} + M_{Q}) V$ $2 \times 50 + 4 \times 0 = (2 + 4) V$ $V = 16, 7 {m s}^{- 1}$
Commented by mr W last updated on 28/Mar/21

$a l l i s c o r r e c t e x c e p t (i v), s i n c e t h e$ $b l o c k P {d o e s n}^{'} t m o v e w i t h c o n s t a n t$ $a c c e l e r a t i o n a f t e r r e l e a s e .$ $p e r i o d T = 2 π \sqrt{\frac{m}{k}} = 2 π \sqrt{\frac{2}{8000}} \approx 0.1 s$ $f o r t h e b l o c k P t o r e t u r n b a c k t o i t s$ $i n i t i a l p o s i t i o n i t n e e d s \frac{T}{4} \approx 0.025 s .$ $a t t h i s p o s i t i o n t h e s p r i n g i s$ $c o m p l e t e l y r e l a x e d a n d l o s s e s$ $c o n n e c t i o n w i t h t h e b l o c k P w h i c h t h e n$ $m o v e s w i t h a c o n s t a n t v e l o c i t y v_{P} :$ $v_{P} = \sqrt{\frac{2 W}{m}} = \sqrt{\frac{2 \times 10}{2}} = \sqrt{10} m / s$ $a l s o a t t i m e t = 0.25 s, t h e b l o c k P h a s$ $t h i s v e l o c i t y t i l l i t c o l l i d e s w i t h b l o c k$ $Q . t h e v e l o c i t y a f t e r c o l l i s i o n i s$ $v_{P + Q} = \frac{M_{P} v_{P}}{M_{P} + M_{Q}} = \frac{2 \times \sqrt{10}}{2 + 4} = \frac{\sqrt{10}}{3} \approx 1.05 m / s$
Commented by I want to learn more last updated on 28/Mar/21

$I really appreciate sirs . God bless you .$
Commented by Olaf last updated on 28/Mar/21

$I uninstall this app .$ $Good continuation sir .$
Commented by Tawa11 last updated on 14/Sep/21

$nice$
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