Answer :
To find the work done by a person walking up a spiral staircase, we convert their weight to Newtons, calculate the vertical distance in meters for one and a half revolutions, and use the work formula. Approximately 3839.29 Joules of work are done by the person.
To calculate the work done by a person walking up a circular staircase, we'll use the formula for work, which is Work (W) = force (f) imes distance (d). In this scenario, the force is the weight of the person due to gravity, and the distance is the vertical height the person climbs.
First, we convert the person's weight from pounds to Newtons, knowing that 1 lb ild equals 4.44822 N. We have:
- Weight = 145 lb imes 4.44822 N/lb ild equals 645.991 N
- Height gained per revolution = 13 ft
- Number of revolutions = 1.5
To find the total height gained, we multiply the height per revolution by the number of revolutions:
- Total height gained = 13 ft imes 1.5 = 19.5 ft
Now, we convert feet to meters because work is measured in Joules (1 ft = 0.3048 m):
- Total height gained in meters = 19.5 ft imes 0.3048 m/ft ild equals 5.9436 m
With the force in Newtons and the distance in meters, we can now calculate the work done:
- Work = 645.991 N imes 5.9436 m
- Work = 3839.2906 Joules
The person does approximately 3839.29 Joules of work by walking up the spiral staircase.
