Answer to Question #116104 in Physics for Higgins

Question

The distance between the sixth and the eleventh floors of a building is 30.0 m. The
combined mass of the elevator and its contents is 1.35 x 103
kg.
a) Find the gravitational potential energy of the elevator when it stops at the eighth
floor, relative to the sixth floor.
b) Find the gravitational potential energy of the elevator when it pauses at the eleventh
floor, relative to the eighth floor.
c) Find the gravitational potential energy of the elevator when it stops at the eleventh
floor, relative to the sixth floor.

Answer 1

a) Height of one floor:

$$h=\frac{30}{11-6}=6\ m$$

$$E=(8-6)mgh=(8-6)(1350)(9.8)(6)\\=1.59\cdot 10^5\ J$$

b)

$$E=(11-8)mgh=(11-8)(1350)(9.8)(6)\\=2.38\cdot 10^5\ J$$

c)

$$E=(11-6)mgh=(11-6)(1350)(9.8)(6)\\=3.97\cdot 10^5\ J$$