Apparent Weight
Drag Force and Terminal Velocity
Apparent Weight
Our perception of weightlessness is really the absence or
reduction of normal (contact) forces acting upon our body.
Conversely, we can feel heavier if the normal (contact) forces
acting on us are larger than normal.
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Apparent Weight in an Elevator
Now suppose you stand on the bathroom scale and ride an
elevator up and down. As you are accelerating upwards and
downwards, the scale reading is different than when you are at
rest and traveling at constant speed.
Which situation does Anna feel the heaviest?
Which situation does she feel the lightest?
B
D
Apparent Weight in an Elevator - Concepts
A
There is no change in motion so the upwards push on
your feet must be equal and opposite to your weight – you
feel normal weight
B
Your body wants to remain at rest but the elevator starts to
move upwards. This imparts more upwards force on your
feet than your weight – you feel heavier
C
A body at rest wants to stay at rest so when the elevator
starts to move down there is less force pushing on your feet
– you feel lighter.
D
Free Fall – You feel weightless
Apparent Weight in an Elevator
Coming Down
a
FNET
Elevator starts
accelerating
downwards
Elevator at
constant speed
downwards
FNET = 0
FNET = m a
(down)
Zero
Acceleration
F N = Fg
FN < F g
FNET = 0
Elevator at rest
Zero
Acceleration
FNET
a
F N = Fg
The normal Force (orange) is what she feels
Elevator is
slowing down to
a stop while
moving down
FNET = m a (up)
F N > Fg
Apparent Weight in an Elevator
Coming Down - Theory
a
FNET
FNET = 0
FNET = m a (down)
FN = Fg = mg
FNET = Fg - FN
Normal
Weight
mg - FN = ma
FN = mg - ma
FN = m(g - a)
Lower
Weight
FNET
a
FNET = 0
FN = Fg = mg
FNET = m a (up)
FNET = FN - Fg
FN -mg = ma
Normal
Weight
FN = ma + mg
FN = m(g + a)
Heavier
Weight
Apparent Weight in an Elevator
Going Up
a
Elevator at rest
Zero
Acceleration
FNET = 0
F N = Fg
a
FNET
Elevator starts
accelerating
upwards
Elevator at
constant speed
upwards
FNET = m a (up)
Zero
Acceleration
FN > F g
FNET = 0
F N = Fg
FNET
Elevator is
slowing down to
a stop while
moving up
FNET = m a
(down)
F N < Fg
Apparent Weight in an Elevator
Going Up
a
FNET = 0
FN = Fg = mg
Normal
Weight
a
FNET
FNET = m a (up)
FNET = FN - Fg
FNET = 0
FNET = m a (down)
FN = Fg = mg
FNET = Fg - FN
FN -mg = ma
FN = ma + mg
FN = m(g + a)
FNET
Normal
Weight
mg - FN = ma
FN = mg - ma
FN = m(g - a)
Heavier
Weight
Lower
Weight
Going up and Down
 In

General:
If your apparent weight is less
• F = m (g – a)

If your apparent weight is more
• F = m (g +a)
 When
the contact force is less your
apparent weight is less, when the contact
force is more your apparent weight is
more.
Terminal Velocity
Consider a skydiver:
1) At the start of his jump the air
resistance is small so he
accelerates downwards.
2) As his speed increases his air
resistance will increase.
3) Eventually the air resistance will be
big enough to equal the skydiver’s
weight. At this point the forces
are balanced so his speed becomes
constant - this is called
TERMINAL VELOCITY
Terminal Velocity
Consider a skydiver:
4) When he opens his parachute the
air resistance suddenly increases,
causing him to start accelerating
upward.
5) Because he is slowing down his air
resistance will decrease again until
it balances his weight. The
skydiver has now reached a new,
lower terminal velocity.
For a typical person, terminal speed is 60
m/s or approximately 135 miles per hour.
A person has to fall over 400 yards
before you really need to start taking
this into account.
Velocity-time graph for terminal velocity…
Parachute opens –
diver slows down
Velocity
Speed
increases…
Terminal
velocity
reached…
Time
New, lower terminal
velocity reached
Diver hits the ground
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