Final answer:
The change in gravitational potential energy of the block as it drops 4 meters is -196.2 J, indicating a loss in GPE. The change in kinetic energy is -16.2 J, which points to a small increase as a result of the tension doing negative work, thereby slightly reducing the conversion of GPE into kinetic energy.
Step-by-step explanation:
To find the change in gravitational potential energy (GPE) for the block-earth system as the block drops 4 meters, we use the formula ΔGPE = mgh, where m is the mass of the block, g is the acceleration due to gravity (9.81 m/s²), and h is the height. The mass (m) is 5 kg and the height (h) is 4 meters. Therefore, the change in GPE is ΔGPE = 5 kg × 9.81 m/s² × 4 m, which results in a change of -196.2 J (the negative sign indicates a loss in GPE).
For the change in kinetic energy (KE), if we assume no other forces except gravity and the tension are doing work on the block (and ignoring air resistance), then the work done by tension (which is opposite to the direction of displacement) must be subtracted from the work done by gravity. Since work equals force times distance, the tension does -45 N × 4 m = -180 J of work. This work done by the tension reduces the amount of gravitational potential energy that is converted into kinetic energy. Thus, the net change in kinetic energy for the block as it descends will be ΔGPE minus the work done by the tension, or -196.2 J - (-180 J) = -16.2 J. This suggests a slight increase in KE as the block was lowered because a small amount of GPE was converted into KE.