Apparent WeightApparent Weight

Drag Force and Terminal VelocityDrag 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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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.

Apparent Weight in an Elevator

Which situation does Anna feel the heaviest? Which situation does she feel the lightest?

B

D

Apparent Weight in an Elevator - Concepts

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.

C

AThere 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

Free Fall – You feel weightlessD

Apparent Weight in an Elevator

Coming Down

Elevator at rest

Zero Acceleration

FNET = 0

FN = Fg

Elevator starts accelerating downwards

FNET = m a (down)

FN < Fg

Elevator is slowing down to a stop while moving down

FNET = m a (up)

FN > Fg

Elevator at constant speed downwards

Zero Acceleration

FNET = 0

FN = Fg

The normal Force (orange) is what she feels

a aFNET

FNET

Apparent Weight in an Elevator

Coming Down - Theory

FNET = 0

FN = Fg = mg

FNET = m a (down) FNET = m a (up)FNET = 0

FN = Fg = mg

a aFNET

FNET

FNET = Fg - FN

mg - FN = ma

FN = mg - ma

FN = m(g - a)

FNET = FN - Fg

FN -mg = ma

FN = ma + mg

FN = m(g + a)

Normal Weight

Lower Weight

Normal Weight

Heavier Weight

Apparent Weight in an Elevator

Going Up

Elevator at rest

Zero Acceleration

FNET = 0

FN = Fg

Elevator starts accelerating upwards

FNET = m a (up)

FN > Fg

Elevator at constant speed upwards

Zero Acceleration

FNET = 0

FN = Fg

Elevator is slowing down to a stop while moving up

FNET = m a (down)

FN < Fg

aa FNETFNET

Apparent Weight in an Elevator

Going Up

aa FNETFNET

FNET = 0

FN = Fg = mg

FNET = 0

FN = Fg = mg

FNET = m a (up)

FNET = FN - Fg

FN -mg = ma

FN = ma + mg

FN = m(g + a)

FNET = m a (down)

FNET = Fg - FN

mg - FN = ma

FN = mg - ma

FN = m(g - a)

Normal Weight

Heavier Weight

Lower Weight

Normal Weight

Going up and DownGoing up and Down

In General:In General: If your apparent weight is less If your apparent weight is less

• F = m (g – a)F = m (g – a) If your apparent weight is moreIf your apparent weight is more

• F = m (g +a)F = m (g +a)

When the contact force is less your When the contact force is less your apparent weight is less, when the contact apparent weight is less, when the contact force is more your apparent weight is force is more your apparent weight is more.more.

Terminal VelocityTerminal 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 VelocityTerminal 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-time graph for terminal velocity…velocity…

Velocity

Time

Speed increases…

Terminal velocity reached…

Parachute opens – diver slows down

New, lower terminal velocity reached

Diver hits the ground

On the Moon

Really Crazy People!!Really Crazy People!!

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