How much work is done by a girl weighing 450N while carrying a 2kg package up a 2m flight of stairs?
Including the work she does lifting herself,
W = 450*H + Mp*g*H
(Mp is the package mass and H is the 2 m elevation change)
= 900 + 2*9.8*2 = 939.2 J
To calculate the amount of work done by the girl, we use the formula:
Work = Force * Distance * cos(angle)
Where:
- Work is measured in joules (J).
- Force is the applied force in newtons (N).
- Distance is the displacement in meters (m).
- Angle is the angle between the direction of the applied force and the displacement.
In this case, the girl is carrying a package up a flight of stairs, which means she is applying a vertical force in the opposite direction of gravity. We can assume that the angle between the force and displacement is 180 degrees.
Given:
- Force (F) = 450 N (weight of the girl)
- Distance (d) = 2 m
- Angle (θ) = 180 degrees
First, let's calculate the work without considering the angle:
Work = Force * Distance
Work = 450 N * 2 m
Work = 900 J
Now, let's consider the angle using the formula:
Work = Force * Distance * cos(θ)
Work = 450 N * 2 m * cos(180°)
Since cos(180°) is -1, we can substitute the value:
Work = 450 N * 2 m * (-1)
Work = -900 J
So, the work done by the girl is -900 joules (J). The negative sign indicates that the work is done against the force of gravity because the girl is lifting the package upward.