Final answer:
The student's reasoning that doubling the height would double the spring compression is incorrect because the elastic potential energy depends on the square of the compression, which means the new spring compression would be the square root of two times the original compression, not double.
Step-by-step explanation:
The student's reasoning is partially correct in the context of energy conservation but does not accurately reflect the relationship between gravitational and elastic potential energy. When the block is lifted to a height of 2h, the gravitational potential energy will indeed increase to double the original potential energy because gravitational potential energy is given by U = mgh where m is mass, g is acceleration due to gravity, and h is height. However, the spring compression will not necessarily double to 2x due to the non-linear nature of elastic potential energy, which depends on the compression squared (Us = 1/2 kx2 where k is the spring constant and x is the compression).
If the initial gravitational potential energy is converted entirely into elastic potential energy (assuming no other forms of energy are involved), the relationship will not be a simple doubling. Instead, the new compression distance x' can be calculated from Ug = Us, leading to mgh = 1/2 kx'2. For double the height, we would have 2mgh = 1/2 kx'2, which means the new compression x' would be the square root of two times x (x' = √2x) assuming that no other energy losses are present and the system is entirely conservative.
The student's reasoning omits the importance of the elastic potential energy's dependence on the square of the compression distance, which leads to incorrect conclusions about the compression of the spring being directly proportional to the height from which the box is released.