when an 81.0 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 3000 j. by how much does the potential energy of an 22.0 kg child increase when the child climbs a normal staircase to the second floor?
To determine the increase in potential energy for the 22.0 kg child climbing a normal staircase to the second floor, we can use the formula:
Potential Energy = mass × acceleration due to gravity × height
Since the height is the same for both cases (climbing to the second floor), we can compare the potential energy change based on the mass difference.
Let's first calculate the potential energy change for the 81.0 kg adult:
Potential Energy (adult) = 3000 J
Mass (adult) = 81.0 kg
Acceleration due to gravity = 9.8 m/s²
Using the formula, we can rearrange it to solve for the height:
Height (adult) = Potential Energy (adult) / (mass (adult) × acceleration due to gravity)
Height (adult) = 3000 J / (81.0 kg × 9.8 m/s²)
Height (adult) ≈ 3.82 meters
Now, we can calculate the potential energy change for the 22.0 kg child:
Mass (child) = 22.0 kg
Height (child) = Height (adult) ≈ 3.82 meters
Acceleration due to gravity = 9.8 m/s²
Using the same formula:
Potential Energy (child) = mass (child) × acceleration due to gravity × height (child)
Potential Energy (child) = 22.0 kg × 9.8 m/s² × 3.82 meters
Potential Energy (child) ≈ 828.54 J
Therefore, the potential energy of the 22.0 kg child increases by approximately 828.54 J when climbing a normal staircase to the second floor.