Question 1
b) i) loss in gpe = 0.785 J ii) gain in epe = 0.392J
c) The loss in gpe is not equal to gain in epe because some heat is produced due to the stretching of the spring.
d) The resultant force at the lowest point = T - mg, where T = k(o.3) . Resultant force = 1.96 N
ii) a = F/m = 4.9 ms-2, but a = w2xo where xo = 0.1 m.
hence w = 7.0 rads-1
iii) the max speed vo = wxo = 0.70 ms-1 .
e) gpe/J : 0, 0.392 , 0.785 ( use h : 0, o.1 m, 0.2 m)
epe/J : 0.883, 0.392 , 0.0981.( use x : 0.3 m, 0.2 m, 0.1 m ,the extension)
ke/J : 0, 0.0981, 0 ( use the max speed in part iii) )
Et /J : 0.883, 0.883, 0.883 ( sum of the three types of energy)
Using the values to mark out the points at the three positions. The gpe is a straight line. The total energy is a horizontal line, the ke is a U shape curve, and the epe is a curve .EPE and GPE meets at the equilibrium with the same value 0.392 J.
