A spiral staircase in a building is in the shape of a helix of radius meters. Between two floors of the building, the stairs make one full revolution and climb by meters. A person carries a bag of groceries up two floors. The combined mass of the person and the groceries is kg and the gravitational force is downward, where is the acceleration due to gravity, in meters per second squared. Calculate the work done by the person against gravity in joules. Enter the exact answer.

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skyluke89 skyluke89 · Answer 1 · 2020-04-15T11:54:54+02:00

Answer:

-5488 J

Explanation:

The work done by the person against gravity is equal to the change in gravitational potential energy.

Therefore we can write:

[tex]W=mg\Delta h[/tex]

where

m is the combined mass of the man + groceries

g is the acceleration due to gravity

[tex]\Delta h[/tex] is the change in height

In this problem we have:

m = 70 kg is the combined mass of the man + groceries

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

[tex]\Delta h =-8 m[/tex], since the man climbed down 2 floors and each floor is 4 meters

Therefore, the work done against gravity is

[tex]W=(70)(9.8)(-8)=-5488 J[/tex]