Freefall

Red Bull Stratos

• On 14 Oct 2012, Felix Baumgartner set the world record for sky diving, diving down 39 km, and reaching a speed of 1360 km/h (368 m/s)

• In this topic, we will study both the kinematics and dynamics of freefall

FREEFALL WITHOUT AIR RESISTANCE

Definitions (to memorize)

• A Gravitational Field is a region in which mass experiences a force due to gravitational attraction

• Gravitational Field Strength (g) is defined as the gravitational force acting per unit mass

• Weight = mass x gravitational field strength

Freefall w/o Air Resistance

• Two videos of freefall without air resistance:• 1) Vacuum: http://www.youtube.com/watch?

v=AV-qyDnZx0A• 2) On the moon:

http://www.youtube.com/watch?v=KDp1tiUsZw8

Freefall w/o Air Resistance

• What did you observe? • When there is no air resistance

1. Objects accelerate downwards when dropped2. This acceleration is the same for ALL OBJECTs,

regardless of mass or size3. This acceleration is called “acceleration due to

freefall”

Freefall w/o Air Resistance• Consider the free body diagram of an object in

freefall• Fresultant = mg

• But, Fresultant = ma• ma = mg• a = g• Recall “g” is called ‘gravitational field strength’.

It is also called ‘acceleration due to freefall’, and it has both units of Nkg-1 as well as ms-2.

mg

Acceleration due to Freefall

• Since acceleration due to freefall = g• And g depends on the strength of the

gravitational field• Therefore, acceleration due to freefall is less

on the moon than on Earth• This explains why in the moon video, the

objects still accelerate downwards, but more slowly compared to on Earth

v-t graph of an object in freefall

• Recall: in a v-t graph, gradient is acceleration• In a freefall (w/o air resistance) situation,

acceleration is constant, hence gradient is constant (i.e. straight line graph)

Scenario 1: Object dropped from rest

If upwards is positive If downwards is positive

v v

t t

Scenario 1: Object dropped from rest

If upwards is positive If downwards is positive

s s

t t

Scenario 2: Object thrown upwards

If upwards is positive If downwards is positive

v v

t t

Scenario 2: Object thrown upwards

If upwards is positive If downwards is positive

s s

t t

Tips for Solving Problems

• Sign convention is important!• Acceleration always acts downwards• If upwards is taken as positive, acceleration

=-10• If downwards is taken as positive, acceleration

= 10

Practice Task 1

• An object was dropped from rest. Determine how long it takes for its velocity to reach 30 ms-1.

Practice Task 2

• A ball was thrown upwards before it fell down a cliff. If the initial velocity of the ball was 15 ms-1, determine the final velocity of the ball after 5 seconds.

FREEFALL WITH AIR RESISTANCE

Plot v-t graph of Felix Baumgartner

• Link: http://www.youtube.com/watch?v=YIj9XGLTGH8

• Start from: 20 s mark of jump (3:56 of video), record velocity every 5 seconds until 50 s mark

v-t graph of Felix Baumgartner

20 25 30 35 40 45 50600

700

800

900

1000

1100

1200

Freefall with Air Resistance

• Stage 1: Object just released from rest, instantaneous velocity zero

• No air resistance, because v = 0• Fresultant = mg

• Fresultant = ma• a = g• Object has a downward acceleration of g (i.e.

10 ms-2)

mg

Freefall with Air Resistance• Most of the time in real life there is air

resistance• Recall for air resistance:

1. Always opposes direction of motion2. The faster the object, the greater the air resistance3. If velocity is zero, there is no air resistance

• When an object is undergoing freefall under air resistance, we can split its motion into 3 different stages

Freefall with Air Resistance

• Stage 2: Object starts to accelerate downwards starts to encounter air resistance

• Fresultant = mg – Fair

• Fresulatnt = ma

• a = g – (Fair/m)• a < g• Still accelerating downwards, but with lower

acceleration

mg

Fair

Freefall with Air Resistance

• Since object is still accelerating• Velocity (downwards) is still increasing• Since Fair increases when velocity increases• Fair keeps on increasing• Until Fair = mg (stage 3)

mg

Fair

Freefall with Air Resistance

• Stage 3: Fair = mg

• Fresultant = 0

• Since Fresultant = 0, object no longer accelerates• Downwards with uniform velocity• This velocity is called terminal velocity

mg

Fair

v-t graph (with Air Resistance)

If upwards is positive If downwards is positive

v v

t t

vT

vT

s-t graph (with Air Resistance)

If upwards is positive If downwards is positive

s s

t t

Parachutes

• A parachute works by increasing the air resistance of a freefalling object

• Usually the parachute is opened when the object is already falling (may or may not be terminal velocity)

Parachutes• The moment the parachute opens, depending

on how fast the object is currently falling, the Fair may be larger than the mg

• Resultant force is upwards• Objects starts to decelerate (but still going

downwards)• As velocity decreases, Fair decreases• Until resultant force is zero again• Terminal velocity (slower than before)

mg

Fair

Quiz 4

Assignment

• Assignment 3b Topic 3• Paper 1 Qn 2, 5, 9, 17• Paper 2 Qn 2

• Assignment 4 Topic 2• Paper 1 Qn 9, 14• Paper 2 Qn 6

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