# Free Fall Motion by liaoqinmei

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• pg 1
```									Free fall motion
1   Three objects are let go from the same
level.
A   The 1-kg object falls fastest.
B   The 3-kg object falls fastest.

C   The combined
1 kg
object falls
fastest.
D   None of the
1 kg    3 kg   3 kg
above.
2       Car A is moving to the left and
decelerating...
… car B is moving to the right and
accelerating.

A   decelerating          B    accelerating
A    decelerating                  B     accelerating
Take left as positive direction, give the
sign of the following quantities:

Car A         Car B
Velocity         +             
Acceleration                     
1    Falling objects
In air, a coin falls faster than a piece of paper.
In a vacuum, they fall at the same rate.
The difference, in air, is due to air
resistance...
having a greater effect on light bodies than on
heavier bodies.
2             Reading graphs
0.8                    s-t graph of free fall
motion
Position (m)

0.6

0.4

0.2

0.20      0.30      0.4   0.50   0.60   0.70
time (s)
v-t graph of free fall motion
3.5
velocity (m/s)   Linear Fit

3.0                    m ( Slope )
b ( Y Intercept )
9.4174
3.0252
r                      0.9975
Standard Deviation m   0.1836
Standard Deviation b   0.0945
2.0
slope <9.8 m s–2
1.0                                                      Due to air
resistance.

0.20      0.30          0.4   0.50            0.60   0.70
time (s)
Q1 In our daily life, the lighter...
In our daily life, the lighter objects
usually fall slower because
A     it is a physical law.
B     it is an illusion.
C     there is air resistance.
D     there is measuring error.
Q2    True or false...
The acceleration of a free falling object
increases as it falls faster and faster. (T/F)
Q3 True or false...
The acceleration due to gravity is larger for
heavier objects on Moon.                 (T/F)
Q4   Draw the s-t, v-t and...
Draw the s-t, v-t and a-t graphs of a freely
falling object from rest. (downwards: +ve.)
s

t
Q4    Draw the s-t, v-t and...
Draw the s-t, v-t and a-t graphs of a freely
falling object from rest. (downwards: +ve.)
s                   v

slope t

point
t
Q4   Draw the s-t, v-t and...
Draw the s-t, v-t and a-t graphs of a freely
falling object from rest. (downwards: +ve.)
v
a
slope
point
t

t
2   Acceleration due to gravity
If resistance is negligible...
… a body falls freely under gravity with
uniform acceleration.

acceleration due to gravity g

Accepted value = 9.8 m s–2

Take g  10 m s–2 for simplicity
2     Acceleration due to gravity
momentarily at rest
a = –10 m s–2
rises up, speed 
a = –10 m s–2
The ball is thrown
vertically upwards
u = 40 m s–1
a = –10 m s–2
2   Acceleration due to gravity

When the ball falls,
its speed  at the
rate of 10 m s–2

Video           Simulation
3     Solving free fall problems
The equations of motion...

for uniformly accelerated motions...

… apply to falling objects.
g  10 m s-2
Example 10
(a)    How long does the stone     Central Plaza
take to reach the ground?

374 m
Example 10
u=0      s = 374 m
a = g = 10 m s–2
t=?

(a)   Applying s = ut + 1 at 2
2
1
374 = 0  t +  10  t   2
2
 t = 8.65 s
Example 10
(b)    With what speed does        Central Plaza
the stone hit the ground?

374 m
Example 10
u=0        s = 374 m
a = g = 10 m s–2
v=?
(b) Applying v 2  u 2 = 2as
v 2  0 = 2  10  374

 v = 86.5 m s1
Example 10
u=0      s = 374 m
a = g = 10 m s–2
v=?

The stone hits the
What happens
if the stone hits      ground with a
your head?         speed of 86.5 m s-1
(or 311 km h-1)!
Example 11
Peter throws a stone vertically upwards
from the ground with a speed of 20 m s–1.
(a) How high does the stone rise?
Example 11
(a)    How high does the stone rise?
Upward journey:
u = 2 m s–1
momentarily at rest
v=0                (at highest point)

a = 10 m s–2 (downwards ve)
s=?

decelerates
as it rises up
Example 11
(a)    How high does the stone rise?
Applying v 2 – u 2 = 2as
v 2
 u2 02  (2) 2
s=          =
2a     2  (10)
= 0.2 m (upwards)
Example 11
(b)    How long does it take to rise up & to
return to the ground?
Applying s = ut + 1 at 2
2
1
0 = 5  t +  (–10)  t     2
2
 t = 0 or t = 0.4 s
The stone is at s = 0 twice initially at 0 s
and on its return to the ground
after 0.4 s.
Example 11
(c)    With what speed does the stone hit the
ground?

Applying v = u + gt
= 2 + (–10)  0.4
= –2 m s1

The stone hits the ground on its return
with a speed of 2 m s-1.
Example 11
(d)    Sketch the (i) s-t graph
(ii) v-t graph
(iii) a-t graph
of the stone’s motion.
Example 11
s-t graph

displacement/m

0.2

time/s
0.2   0.4
Example 11
v-t graph

velocity/m s-1

2

time/s

–2
0.2   0.4
Example 11
a-t graph

acceleration/m s-2

time/s

–10
(For questions 1 to 5.) A ball is fired upwards
with u = 5 m s1 from the top of a building...
Q1 When the ball goes up...
When the ball goes up, the speed it loses in
10 m s–1
each second is __________.
A ball is fired upwards with u = 5 m s–1
from the top of a building.

It hits the ground 2 s later.
(Take g = 10 m s–2.
Neglect air resistance.)
Q2 When the ball falls down...
When the ball falls down, the speed it gains in
10 m s–1
each second is _________.

A ball is fired upwards with u = 5 m s–1
from the top of a building.

It hits the ground 2 s later.
(Take g = 10 m s–2.
Neglect air resistance.)
Q3 True or false...
True or false: Its velocity changes direction as
it passes the highest point.             (T/F)

A ball is fired upwards with u = 5 m s–1
from the top of a building.

It hits the ground 2 s later.
(Take g = 10 m s–2.
Neglect air resistance.)
Q4 True or false…
True or false: Its acceleration is zero at the
highest point.                             (T/F)

A ball is fired upwards with u = 5 m s–1
from the top of a building.

It hits the ground 2 s later.
(Take g = 10 m s–2.
Neglect air resistance.)
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)

A    s = 0 as it hits the ground.
v2 = u2 + 2as = 52 + 0 = 25
v = 5 m s-1 downwards
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)

B     v = u + gt
= 5 + 10  2 = 25 m s1
The velocity is 25 m s1 downwards.
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)

C   First, consider the rise.
It momentarily stops at the highest point:
t = (0  u)/a = (0  5)/(10) = 0.5 s
Then, consider the fall.
v = 0 + at = 0 + a  (2  t)
= 0 + (10)  (2  0.5) = 15 m s1
The velocity is 15 m s1.
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground (Take upward direction as +ve)

A    s = 0 as it hits the ground...
B    v = u + gt...
C    First, consider the rise.
It momentarily stops...

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