Question

A spiral staircase in a building is in the shape of a helix of radius 5 meters. Between two oors of the building, the stairs make one full revolution and climb by 4 meters. A person carries a bag of groceries up two oors. The combined mass of the person and the groceries is 70 kg and the gravitational force is 70g downward, where g is the acceleration due to gravity. Use a line integral to calculate the work done by gravity against the person.

Answer 1

Answer:

2744Nm

Explanation:

The gravitational field is conservative. The gravitational force only acts on a vertical direction. Hence, independently of the form of the trajectory, the work done by the gravity against the person demands the calculation of the integral of the force multiplied by the vertical displacement of the person:

$W_g=\int_0^{4}Mgdz=Mg[4]=(70kg)(9.8\frac{m}{s^2})(4m)=2744Nm$

where we have taken that the displacement of the person h=z and df=dz.

hope this helps!!