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 (
). The change in potential energy experimented by a particle (
), measured in joules, is:
(1)
Where:
- Mass, measured in kilograms.
- Gravitational acceleration, measured in meters per square second.
,
- Initial and final height with respect to zero reference, measured in meters.
Please notice that
is the weight of the particle, measured in newtons.
a) If we know that
,
,
and
, then the change in potential energy is:
![\Delta U_{g} = (3\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (4.1\,m-0\,m)](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20%283%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%284.1%5C%2Cm-0%5C%2Cm%29)
![\Delta U_{g} = 120.626\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20120.626%5C%2CJ)
The change in potential energy of a 3.0 kilograms backpack carried up the stairs.
b) If we know that
,
and
, then the change in potential energy is:
![\Delta U_{g} = (650\,N)\cdot (0\,m-4.1\,m)](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20%28650%5C%2CN%29%5Ccdot%20%280%5C%2Cm-4.1%5C%2Cm%29)
![\Delta U_{g} = -2665\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20-2665%5C%2CJ)
The change in potential energy of a persona with weight 650 newtons that descends the stairs is -2665 joules.