(a) The work done on the block by the gravitational force is equal to the change in the gravitational potential energy of the block. The gravitational potential energy of the block is equal to mgh, where m is the mass of the block (250 g), g is the acceleration due to gravity (9.8 m/s2), and h is the height from which the block is dropped. Since the block is dropped from rest, the change in gravitational potential energy is equal to mgh. Therefore, the work done on the block by the gravitational force is equal to 250 g x 9.8 m/s2 x 12 cm = 294 J.
(b) The work done on the block by the spring force is equal to the change in the elastic potential energy of the spring. The elastic potential energy of the spring is equal to 1/2 kx2, where k is the spring constant (2.5 N/cm) and x is the compression of the spring (12 cm). Therefore, the work done on the block by the spring force is equal to 1/2 x 2.5 N/cm x (12 cm)2 = 180 J.
(c) The speed of the block just before it hits the spring can be calculated using the equation v2 = 2gh, where v is the speed of the block, g is the acceleration due to gravity (9.8 m/s2), and h is the height from which the block is dropped (12 cm). Therefore, the speed of the block just before it hits the spring is equal to √2 x 9.8 m/s2 x 12 cm = 17.3 m/s.