A 96lb boy is standing in an elevator. Find the force on the boy's feet when the elevator (a) stands still (b) moves downward at a constant velocity of 3 ft/d (c) accelerates downward with an acceleration of 4.0 ft/s2, and (d) accelerates upward with an acceleration of 4.0ft/s2

mass of boy, m = 96 lb

acceleration due to gravity, g = 32 ft/s²

(a) When the elevator is stands still

Force, F = m g

F = 96 x 32 = 3072 pounds

(b) When the elevator moves with constant velocity

F = mg = 3072 pounds

(c) When the elevator moves downwards with constant acceleration

F = mg - ma

F = 96 (32 - 4)

F = 2688 pounds

(d)

When the elevator moves upwards with constant acceleration

F = mg + ma

F = 96 (32 + 4)

F = 3456 pounds

a) When the elevator is at rest

R = mg

R = force on the boy's feet = 96 x 32

= 3072 unit.

b) When the elevator moves with uniform velocity, net force on the boy = 0

R = mg

force on the boy's feet = 96 x 32

= 3072 unit

c) When the elevator moves with acceleration a downwards

Reaction force R = mg - ma

= m (g-a)

= 96 (9.8 - 4)

= 556.8 unit

d)

When the elevator moves with acceleration a upwards

Reaction force R = mg + ma

= m (g+a)

= 96 (9.8 + 4)

= 1324.8 poundal