Final answer:
The change in potential energy is calculated with the formula ΔPE = mgh, which represents the energy difference an object experiences due to a change in vertical position. It simplifies complex calculations involving forces across paths by focusing on changes in height and mass only.
Step-by-step explanation:
The formula for calculating the change in potential energy is given by ΔPE = mgh, where m stands for mass, g is the acceleration due to gravity, and h is the change in height. This formula simplifies the calculation of energy changes due to vertical movement, making it much easier than calculating the work done along a path which may be complex.
To demonstrate, if an object like a car is raised to a higher elevation, its potential energy increases. For instance, a car with a mass of 1360 kg that is parked at a height of 36.6 m above the street level would have a potential energy calculated as PE = mgh, which in this case is PE = (1360 kg) * (9.81 m/s²) * (36.6 m).
Similarly, if a truck descends a hill, the change in its gravitational potential energy can be calculated using the same formula. For example, for a truck of mass 10,000 kg going downhill from a height of 75.0 m, the change in potential energy would be ΔPE = mgh = (10,000 kg) * (9.80 m/s²) * (75.0 m) = 7.35 × 10⁶ J.