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 calculate the change in potential energy, we need to use the formula:
ΔPE = m * g * h
where ΔPE is the change in potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the staircase.
First, let's calculate the acceleration due to gravity (g) which is approximately 9.8 m/s².
Now, we can calculate the change in potential energy (ΔPE) for the adult using the given information:
ΔPE(adult) = m(adult) * g * h
3000 J = (81.0 kg) * (9.8 m/s²) * h
To find h, we rearrange the equation:
h = 3000 J / (81.0 kg * 9.8 m/s²)
h ≈ 3.77 meters
Now, we can calculate the change in potential energy for the child using the same formula:
ΔPE(child) = m(child) * g * h
ΔPE(child) = (22.0 kg) * (9.8 m/s²) * 3.77 meters
Now, we can calculate the ΔPE(child) value:
ΔPE(child) ≈ 808.876 J
Therefore, the potential energy of the 22.0 kg child increases by approximately 808.876 J when climbing a normal staircase to the second floor.