Final answer:
The maximum speed of the object can be found using the principle of conservation of energy. The distance the object drops before coming to rest momentarily is equal to the maximum compression of the spring. The energy stored in the spring can be compared with the gravitational potential energy of the object.
Step-by-step explanation:
(a) To find the maximum speed of the object, we can use the principle of conservation of energy. When the object is at its maximum speed, all of its potential energy has been converted into kinetic energy. The potential energy of the object is given by the formula PE = mgh, where m is the mass of the object (0.12 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the object from its starting position. In this case, h is equal to the distance the object dropped before coming to rest momentarily. So, we need to find h first.
(b) The distance the object drops before coming to rest momentarily is equal to the maximum compression of the spring. The potential energy at this point is completely converted into potential energy of the spring, given by the formula PE = 1/2kx^2, where k is the force constant of the spring (40 N/m) and x is the maximum compression of the spring. We can equate the potential energy of the object to the potential energy of the spring to find x.
(c) To find the energy stored in the spring by this stretch, we can use the formula for potential energy of the spring mentioned earlier. To compare it with the gravitational potential energy, we need to find the potential energy of the object at its maximum speed using the formula mentioned in part (a).
As for where the rest of the energy might go, some of it might be converted into other forms of energy such as sound or heat due to various factors like air resistance or internal friction within the system.