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APPARENT WEIGHT AND ACTUAL WEIGHT:

 

Fg:  Actual weight: the force exerted by a gravitational field.  Actual weight of an object will be constant unless mass of the object and gravitational field strength change.

Fn:  Apparent weight:   the normal force exerted on the object by a body with which object is in contact.

 

EXAMPLE:

You are inside an elevator.
m:  Your mass = 70 kg

Let Up direction be positive and Down direction be negative

Fg:  Actual weight = m.g = (70 kg)(- 9,80 m/s2) = - 686 N = 686 N [down]

 Fnet =  Fg + Fn

 Fn = Fnet - Fg

 

CASE 1:  The elevator does not move, or it moves with a constant velocity, up or down:

In this case net force will be zero

 Fnet =  Fg + Fn = 0

 Fn = 0 - Fg

Fn = - Fg = = 686 N

Normal force or Apparent weight:  Fn =  686 [up]

 

CASE 2:  The elevator accelerates upward, example:  a = 5 m/s2 [up]

Fnet =  m.a = (70 kg)(5 m/s2) = 350 N = 350 N [up]

 Fn = Fnet - Fg

 Fn = 350 N - (- 686 N) = 1036 N

Normal force or Apparent weight:  Fn = 1036 [up]

 

CASE 3:  The elevator accelerates downward, example:  a = 5 m/s2 [down]

Fnet =  m.a = (70 kg)(-5 m/s2) = - 350 N = 350 N [down]

 Fn = Fnet - Fg

 Fn = - 350 N - (- 686 N) = 336 N

Normal force or Apparent weight:  Fn = 336 [up]

 

CASE 4:  The line of the elevator is broken (free fall), a = g = 9.8 m/s2 [down]

Fnet =  m.a = (70 kg)(-9.8 m/s2) = - 686 N = 686 N [down]

 Fn = Fnet - Fg = - 686 N - (- 686 N) = 0

Normal force or Apparent weight:  Fn = 0 (You feel weightless.)