Question

There are three different ways to get from location A to location E in the diagram below. In path 1, you take an elevator directly from location A straight up to location E. In path 2, you walk from A to B, climb a rope from B to C, then walk from C to E. In path 3, you walk from location A to D, then climb a ramp up to location E. The following questions focus on the work done on a 68 kg person by the Earth while following each of these paths.

Taking the origin at location A, the coordinates of the other locations are: _B =  -3, 0, 0 ; _C =  -3, 18, 0 ; _D =  48, 0, 0 ; _E> =  0, 18, 0 .

(a) Path 1 (A to E): What is the displacement vector Δ for the path from A to E on the elevator?
Δ =

m
(b) What is the gravitational force acting on the person along path 1, as a vector?
=

N

(c) What is the work done by the gravitational force of the Earth on the 68 kg person during the elevator ride from A to E?
W₁ = •Δ = J


(d) Path 2 (A to B to C to E): What is the work done by the gravitational force of the Earth on the person as he walks from A to B?
W_A→B = J
(e) What is the work done by the gravitational force of the Earth on the person as he climbs from B to C?
W_B→C = J
(f) What is the work done by the gravitational force of the Earth on the person as he walks from C to E?
W_C→E = J
(g) What is the total work done by the gravitational force of the Earth on the person as the person goes from A to E along path 2?
W₂ = J


(h) Path 3 (A to D to E): What is the work done by the gravitational force of the Earth on the person as he walks from A to D?
W_A→D = J
(i) What is the work done by the gravitational force of the Earth on the person as he climbs from D to E?
W_D→E = J
(j) What is the total work done by the gravitational force of the Earth on the person as the person goes from A to E along path 3?
W₃ = J

(k) You calculated the work done by the gravitational force of the Earth on the person along three different paths. How do these quantities compare with each other?

W₁ < W₂ < W₃W₁ = W₂ = W₃    W₁ > W₂ > W₃W₃ > W₁ = W₂

Answer 1

i) work done from D to E= Work done from A to E=-11995.2 J

j) total work done from A to E in path 3= -11995.2J

k) work done in all the three paths is same because gravitational forec is conservative, whose work is independent of path followed