An airplane passenger carries a 260 N suitcase up the stairs, a displacement of 3.80 m vertically, and 4.30 m horizontally.
(a) How much work does the passenger do?
(b) The same passenger carries the same suitcase back down the same stairs. How much work does the passenger do now?
work= mg*height
this time,gravity does work on suitcase,so it is negative.
So how am I supposed to use the heights given from the problem? Subtract 4.30 m from 3.80 m?
To find the work done by the passenger, we first need to understand the equation for work.
The formula for work is given by:
Work = Force * displacement * cos(theta)
where Force is the applied force, displacement is the distance traveled, and theta is the angle between the applied force and the displacement.
In this case, the passenger is carrying the suitcase vertically and then horizontally. Let's break down the problem into two parts: vertical and horizontal displacement.
(a) Vertical Displacement:
The suitcase is carried vertically, up the stairs, for a displacement of 3.80 m. The force exerted by the passenger is the weight of the suitcase, given as 260 N.
Vertical Work = Force * displacement * cos(theta)
Since the force and displacement are in the same direction (vertical upward), the angle between them is 0 degrees. Therefore, cos(theta) = 1.
Vertical Work = 260 N * 3.80 m * 1
Vertical Work = 988 N*m
(b) Horizontal Displacement:
The suitcase is then carried horizontally for a displacement of 4.30 m. In this case, the force and displacement are perpendicular to each other, so the angle between them is 90 degrees. Therefore, cos(theta) = 0.
Horizontal Work = Force * displacement * cos(theta)
Horizontal Work = 260 N * 4.30 m * 0
Horizontal Work = 0 N*m
(c) Total Work:
To find the total work done by the passenger, we need to add the vertical and horizontal work together.
Total Work = Vertical Work + Horizontal Work
Total Work = 988 N*m + 0 N*m
Total Work = 988 N*m
So, the passenger does a total work of 988 N*m in carrying the suitcase up the stairs.