A9.10-kg box is sliding across the horizontal floor of an elevator. the coefficient of kinetic friction between the box and the floor is 0.375. determine the kinetic frictional force that acts on the box when the elevator is (a) stationary, (b) accelerating upward with an acceleration whose magnitude is 1.69 m/s2, and (c) accelerating downward with an acceleration whose magnitude is 1.69 m/s2

Answer

given,

mass of the box = 9.1 kg

kinetic friction coefficient = 0.375

acceleration = 1.69 m/s²

kinetic frictional force on the box = ?

If the elevator is stationary, the kinetic frictional force is

F = µ m g

F = 0.375 × 9.1 × 9.81

F = 33.48 N.

If the elevator is accelerating upward at 1.88 m/s^2, we add the acceleration to the acceleration due to gravity. The force is

F = µ m (g+a)

F = 0.375 x  9.1 x (9.81 + 1.69)

F = 0.375 x  9.1 x 11.5

  F= 42.31 N

If the elevator is accelerating downward, we subtract.

F = µ m (g-a)

F = 0.375 x  9.1 x (9.81 - 1.69)

F = 0.375 x  9.1 x 8.12

  F= 27.71 N

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day