Mass 3.0 kg Spring stiffness constant (k) = 950 N/m Initial displacement of block = 0.150 m Calculate (a) the inital elastic PE and (b) the gravitional PEgained as the mass rises .15m. Then use the resuylt to calculate(c) the finial KE and (d) the finial velocity. I got this question wrong on the homework. The teacher gave usthe answer, but i dont know how to find them. The answers are (a)10.7J (b) 4.4J (c) 6.3J, (d) 2.0m/s. Mass 3.0 kg Spring stiffness constant (k) = 950 N/m Initial displacement of block = 0.150 m Calculate (a) the inital elastic PE and (b) the gravitional PEgained as the mass rises .15m. Then use the resuylt to calculate(c) the finial KE and (d) the finial velocity. I got this question wrong on the homework. The teacher gave usthe answer, but i dont know how to find them. The answers are (a)10.7J (b) 4.4J (c) 6.3J, (d) 2.0m/s.
Explanation / Answer
Mass m = 3.0 kg Spring stiffness constant (k) = 950 N/m Initial displacement of block x = 0.150m (a). Initial elastic potential energy = ( 1/ 2) k x ^2 = 0.5 * 950 * 0.15 ^ 2 = 10.6875 J E ~ 10.7 J (b). Gravitational potential energy gained as the mass rises0.15 m is = mgh = 3*9.8*0.15 E' = 4.41 J (c). Final kinetic energy K.E = E - E' Since from law of conservation of energyE = E ' + K.E =10.6875 J - 4.41 J = 6.2775 J (d). we know K.E = ( 1/ 2) m v ^ 2 from this final velocity v = [ 2 * K.E / m] = 2.045 m / s ~ 2 m / s