Question

Consider the system on the horizontal plane as shown below. -0.4 m 0.4 m k = 800 N/m k = 800 N/m WWWWWW W 10 kg & Il yu1 = 2 m/s N 0.3 m LU2 a) The 10-kg collar slides on the smooth vertical rod and has a velocity vi = 2 m/s in position A where each spring is stretched 0.1 m. Calculate the velocity v2 of the collar as it passes point B. b) Find the position of the collar below A where its speed is zero. c) Find the position of the collar above A where its speed is zero. d) Comment on the conservation of the mechanical energy for the system. e) Assume that the collar moves with the given velocity vi and reaches the position in part b and continues to its motion by reaching the position in part c and repeats this sequence of motion. Find the frequency of the motion. Hint: You can find the equation of motion and use it to find the frequency of oscillations.

I need all option clearly

Answer 1

loką lokg orymme 0.4m 10. 3m 10.44 0.32 0.5m mm - zo – - - - - - - TU2 duitially vox hame potential energy stored in a springs, deve (PE); to gravitation ie myth, kinetic energy (KE); 1 mv? finally boo only home (PE) and Potential energy stored in spring since we are considering point 2 as a datum Stretch in spring initially : 04-0.3m= 0lm = 1 of retch – finally = 0.5-0.3 = 0.24 = x2 ay conservation of freegy Energy at 1 = Energy at 2 mut & might + 2 x( {kx) = 1 m 2 + 2x ( 1 (K 22 ) ) 1 x for 22 + 10x 9.81 x 0.3 + 2x2 x 800 ( 0.1 20 2² ) & Ixlox V₂2 12 2 - 5.086 (12=2.255 me

22 spring stretch at 3 0.4m AAAA V hz +0.16 – 0.3 – 3. 7 22 илллллли z o At 33 there is only pe stored in sprung 80 By Conservation of Greagey righ3 + 2 x 2 x K x + 1 mor - 2x zx k az 10x 9.81 x hy of fx zx 80 x 0-12 + 2x10x2² - 8oor (h3 +0.16 - 003) 10awana 98.163 ito +20 = 800 { hot 0.16 + (0.3) ² 24 0.3 x 503 +0.16) 0.035 + 0.12 2625 hz = hart 0.25 -0.6 x 2 +0.16 By Aquaving on Both sides and rearranging wag + h (-0.24525) oat hy (0.0776) + 0.0024 hz - 0.0575 to polling for ha Tha= – 29.73m, 27.98m , other two solutions are emaginary keer in mind that hz is in reference with Z=0 se at (33) d) Mechanical energy of the system remains Constant or - conserned during the whole process or movement of collar.