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Freefall
Lesson Structure
• Part 1 – Freefall without Air Resistance – Dynamics – v-‐t graph
• Part 2 – Freefall with Air Resistance – Plot Baumgartner’s v-‐t graph – Dynamics: 3 stages of freefall (w/AR) – v-‐t graphs
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 kinemaScs and dynamics of freefall
Plot v-‐t graph of Felix Baumgartner
• Link: hTp://www.youtube.com/watch?v=YIj9XGLTGH8
• Start from: 20 s mark of jump (3:56 of video), record velocity every 5 seconds unSl 50 s mark
Freefall w/o Air Resistance
• Two videos of freefall without air resistance: • 1) In vacuum: hTp://www.youtube.com/watch?v=AV-‐qyDnZx0A
• 2) On the moon: hTp://www.youtube.com/watch?v=KDp1SUsZw8
Freefall w/o Air Resistance
• What did you observe? • When there is no air resistance
1. Objects accelerate downwards when dropped 2. This acceleraSon is the same for ALL OBJECTs,
regardless of mass or size 3. This acceleraSon is called “acceleraSon 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 ‘gravitaSonal field strength’. It is also called ‘acceleraSon due to freefall’, and it has both units of Nkg-‐1 as well as ms-‐2.
mg
AcceleraSon due to Freefall
• Since acceleraSon due to freefall = g • And g depends on the strength of the gravitaSonal field
• Therefore, acceleraSon due to freefall is less on the moon than on Earth
• This explains why in the moon video, the objects sSll 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 acceleraSon • In a freefall (w/o air resistance) situaSon, acceleraSon is constant, hence gradient is constant (i.e. straight line graph)
Scenario 1: Object dropped from rest
If upwards is posi-ve If downwards is posi-ve
v v
t t
Scenario 1: Object dropped from rest
If upwards is posi-ve If downwards is posi-ve
s s
t t
Scenario 2: Object thrown upwards
If upwards is posi-ve If downwards is posi-ve
v v
t t
Scenario 2: Object thrown upwards
If upwards is posi-ve If downwards is posi-ve
s s
t t
Tips for Solving Problems
• Sign convenSon is important! • AcceleraSon always acts downwards • If upwards is taken as posiSve, acceleraSon =-‐10
• If downwards is taken as posiSve, acceleraSon = 10
PracSce Task 1
• An object was dropped from rest. Determine how long it takes for its velocity to reach 30 ms-‐1.
PracSce Task 2
• A ball was thrown upwards before it fell down a cliff. If the iniSal velocity of the ball was 15 ms-‐1, determine the final velocity of the ball aper 5 seconds.
Freefall with Air Resistance • Most of the Sme in real life there is air resistance
• Recall for air resistance: 1. Always opposes direcSon of moSon 2. The faster the object, the greater the air
resistance 3. If velocity is zero, there is no air resistance
• When an object is undergoing freefall under air resistance, we can split its moSon into 3 different stages
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 acceleraSon of g (i.e. 10 ms-‐2)
mg
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 • SSll acceleraSng downwards, but with lower acceleraSon
mg
Fair
Freefall with Air Resistance
• Since object is sSll acceleraSng • Velocity (downwards) is sSll increasing • Since Fair increases when velocity increases • Fair keeps on increasing • UnSl 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 posi-ve If downwards is posi-ve
v v
t t
vT
vT
s-‐t graph (with Air Resistance)
If upwards is posi-ve If downwards is posi-ve
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 sSll going downwards)
• As velocity decreases, Fair decreases • UnSl resultant force is zero again • Terminal velocity (slower than before)
mg
Fair
Quiz 4
Assignment 4
• TYS Topic 2 • Paper 1 Qn 10, 11, 15 • Paper 2 Qn 3
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