Drag Force and Terminal Velocity 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. maxair at cedar point – YouTube Drop Tower at KI – YouTube ME ON DROP ZONE - YouTube

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. B Which situation does Anna feel the heaviest? Which situation does she feel the lightest? D

Apparent Weight in an Elevator - Concepts 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 A 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 FNET a a FNET Elevator starts accelerating downwards FNET = m a (down) FN < Fg Elevator at rest Zero Acceleration FNET = 0 FN = Fg Elevator at constant speed downwards Zero Acceleration FNET = 0 FN = Fg Elevator is slowing down to a stop while moving down FNET = m a (up) FN > Fg The normal Force (orange) is what she feels

Apparent Weight in an Elevator Coming Down - Theory FNET a a FNET FNET = 0 FN = Fg = mg FNET = m a (down) FNET = 0 FN = Fg = mg FNET = m a (up) FNET = Fg - FN FNET = FN - Fg Normal Weight mg - FN = ma FN -mg = ma Normal Weight FN = mg - ma FN = ma + mg FN = m(g - a) FN = m(g + a) Lower Weight Heavier Weight

Apparent Weight in an Elevator Going Up a a FNET FNET 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

Apparent Weight in an Elevator Going Up a a FNET FNET FNET = m a (up) FNET = 0 FN = Fg = mg FNET = 0 FN = Fg = mg FNET = m a (down) FNET = FN - Fg FNET = Fg - FN FN -mg = ma Normal Weight mg - FN = ma FN = ma + mg Normal Weight FN = mg - ma FN = m(g + a) 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: 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… On the Moon Diver hits the ground New, lower terminal velocity reached Time

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