hand writ/e and show all work and steps please

Note for question 35. (this problem cannot be solved using Hooke's law, because when the spring is stretched at the point we are looking at, it is not in equilibrium, it is accelerating itself back upwards and changing direction. Therefore, energy needs to be used. )

35. (II) A spring with k = 83 N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position? 39. (II) A vertical spring {ignore its mass), whose spring constant is 875 Mm, is attached to a table and is compressed down by 0.160 m. (a) What upward speed can it give to a 0.380kg ball when released? (b) How high above its original position (spring compressed) will the ball fly? (II) In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start? 51. (ll) What will a spring scale read for the weight of a 58.0kg woman in an elevator that moves (a) upward with constant speed 5.0 m/s, (b) downward with constant speed 5.0 m/s, (c) with an upward acceleration 0.23 g, (d) with a downward acceleration 0.23 g, and (e) in free fall? 57. (I) Neptune is an average distance of 4.5 x 109 km from the Sun. Estimate the length of the Neptunian year using the fact that the Earth is 1.50 x 108 km from the Sun on average. 59. (I) Use Kepler's laws and the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth's surface. 65. (II) Holley's comet orbits the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5-45). Estimate the greatest distance of the comet from the Sun. Is it still \"in" the solar system? What planet's orbit is nearest when it is out there? _ _ ._ A ._ __ Halley's comet "' \\ Sun 2' FIGURE 5-45 . ' Problem 65. .. -- -" "' 31. (ll) Two objects attract each other gravitationally with a force of 2.5 x 10'10 N when they are 0.25 m apart. Their total mass is 4.00 kg. Find their individual masses. 39. (ll) Calculate the effective value of g, the acceleration of gravity, at (a) 6400 m, and (b) 6400 km, above the Earth's surface. (II) In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start