Question

A horizontal spring with spring constant 30 N/m is compressed by 5 cm by a 10 gram mass. After the mass is released, it accelerates due to the potential energy of the spring. Use conservation of energy to determine what speed the 10 gram mass reaches after being pushed by the spring Answer in units of m/s and round to 3 significant figures

Answer 1

spering irrimi mass Initial state Horomo Final state se is compression in spring Mass = M = 10g = 10x10 -3 kg = 1866-2 kg compression = x=5cm = 5x10-2m spring constant of spring = = 30 N/m Letr be the speed of mass m In final state spring has only potential energy (Pi) and no Kinetic energy (K) = PI = 1 kx2 and k, = 0 when mass m is released then it has no potential energy (P2) and has only Kinetic energy (K2) =) P2 zo and K₂ = I mv2 By conservation of energy Energy before = Energy after =) Pi + k, = P2 +K2 = 4 Ka²+0=0+ I muz = kx2 = mv2 = v2= kx? >> VS * = v= 10-2 (5x162) mis -) V=130x702 xs xio-2 mis = 5.477 x70x5X10-2 = v=2.7385 m/s ~ 2.74 m/s (3 significant figuere) ↑