Final answer:
The passenger does 903 Joules of work when carrying a 215-N suitcase up 4.2 meters vertically up the stairs due to gravity, and zero work against gravity when bringing the suitcase down, if done at constant velocity.
Step-by-step explanation:
Work Done by a Passenger Carrying a Suitcase Up and Down the Stairs
To determine how much work the passenger does when carrying a 215-N suitcase up the stairs, we must consider the vertical displacement only. The horizontal displacement does not contribute to work against gravity. Work is calculated by the formula:
Work = Force × Displacement × cos(θ)
Where θ is the angle between the force and displacement direction. Since the force due to weight is acting vertically downward, and the displacement is vertical upwards, θ is 0 degrees, and the cosine term equals 1. Therefore, the work done is:
Work = 215 N × 4.20 m × 1 = 903 N·m or Joules
When the passenger brings the same suitcase down the stairs, no work is done against gravity. Instead, gravity does work on the suitcase. The passenger may do work to control the descent, but this is not calculated the same way, and if the suitcase is just lowered at a constant velocity, the work done by the passenger against gravity is zero since the displacement is in the direction of the gravitational force.
In summary, the passenger does 903 Joules of work lifting the suitcase up the stairs, and zero work related to gravity when bringing it down, if done at constant velocity.