Answer :
Answer:
a) The change in potential energy of a 3.0 kilograms backpack carried up the stairs.
b) The change in potential energy of a persona with weight 650 newtons that descends the stairs is -2665 joules.
Explanation:
Let consider the bottom of the first floor in a building as the zero reference ([tex]z = 0\,m[/tex]). The change in potential energy experimented by a particle ([tex]\Delta U_{g}[/tex]), measured in joules, is:
[tex]\Delta U_{g} = m\cdot g\cdot (z_{f}-z_{o})[/tex] (1)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]z_{o}[/tex], [tex]z_{f}[/tex] - Initial and final height with respect to zero reference, measured in meters.
Please notice that [tex]m\cdot g[/tex] is the weight of the particle, measured in newtons.
a) If we know that [tex]m = 3\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]z_{o} = 0\,m[/tex] and [tex]z_{f} = 4.1\,m[/tex], then the change in potential energy is:
[tex]\Delta U_{g} = (3\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (4.1\,m-0\,m)[/tex]
[tex]\Delta U_{g} = 120.626\,J[/tex]
The change in potential energy of a 3.0 kilograms backpack carried up the stairs.
b) If we know that [tex]m\cdot g = 650\,N[/tex], [tex]z_{o} = 4.1\,m[/tex] and [tex]z_{f} = 0\,m[/tex], then the change in potential energy is:
[tex]\Delta U_{g} = (650\,N)\cdot (0\,m-4.1\,m)[/tex]
[tex]\Delta U_{g} = -2665\,J[/tex]
The change in potential energy of a persona with weight 650 newtons that descends the stairs is -2665 joules.