Transcript V - Learning

Falling Objects
• Two different object with different masses
will FALL at the ………………………….
1kg
10kg
1kg 1kg 1kg 1kg 1kg
10N
100 N
10N 10N 10N 10N 10N
• The force of gravity on 1kg of mass is ………….. N.
• Each unit of mass has the ………………………….!
• Each mass unit will have the ………………………...
Falling Objects
• Two different object with different masses
will FALL at the same RATE.
1kg
10kg
1kg 1kg 1kg 1kg 1kg
10N
10Nkg10N 10N
10N 10N 100
• The force of gravity on 1kg of mass is 10 N.
• Each unit of mass has the same force on it!
• Each mass unit will have the SAME ACCELERATION.
Finding “g” by Pendulum
• The cotton is burnt to release the plumb bob.
• The vertical distance is measured to where the
plumb bob …………………………...
• The distance is fallen in ……………………..
……………………………………………..
• Readings: …………….., …………………
S = ………………………
• The time is measured for ……… complete
oscillations to give a ……………….. reading.
• If the time for 10 oscillations is 16,6s - the
time for ¼ oscillation is …………………...
• If the distance fallen is …………..m.
• Acceleration or “g” can then be calculated.
a = …………………………………………….
s
Finding “g” by Pendulum
• The cotton is burnt to release the plumb bob.
• The vertical distance is measured to where the
plumb bob hits the metre stick.
• The distance is fallen in one quarter of an
oscillation.
• Readings: Time, distance
x = vit + (1/2)at2
• The time is measured for ten complete
oscillations to give a more accurate reading.
• If the time for 10 oscillations is 16,6s - the
time for ¼ oscillation is 16,6/40 = 0,415s.
• If the distance fallen is 0,84m.
• Acceleration or “g” can then be calculated.
a = (1/2)at2 = 2(0.84)/(0.415) = __9.75_m/s
s
Falling bodies
Acceleration due to gravity
• Bodies accelerate downwards at the ……………… when
allowed to fall freely under the influence of gravity.
“g” = …………………………………………….
• Objects fall at this rate of “g” = ………………….(for our
purposes we use 10m.s-2)
• (This means every second the object is going
………………….. than it was the second before.)
Falling bodies
Acceleration due to gravity
Motion of a falling Body Spreadsheet
• Bodies accelerate downwards at the same rate when
allowed to fall freely under the influence of gravity.
“g” = the acceleration caused by gravity.
• Objects fall at this rate of “g” = 9,8m.s-2 (for our purposes
we use 10m.s-2)
• (This means every second the object is going 10m/s
FASTER than it was the second before.)
Motion of Falling object
Time (s)
Displacem
ent (m)
Average
Velocity
Instantaneou
s Velocity
(m.s-1)
Accelerati
on (m.s-2)
0
0
0
0
0
1
5
2
20
3
45
80
4
5
6
125
180
Motion of Falling object
Time (s)
Displacem
ent (m)
Average
Velocity
0
0
0
1
5
5
2
20
10
3
45
80
15
20
125
25
180
30
4
5
6
Instantaneou
s Velocity
(m.s-1)
Accelerati
on (m.s-2)
Motion of Falling object
Time (s)
Displacem
ent (m)
Average
Velocity
Instantaneou
s Velocity
(m.s-1)
0
0
0
1
5
5
0
10
2
20
10
20
3
45
80
15
20
30
125
25
180
30
4
5
6
40
50
60
Accelerati
on (m.s-2)
Motion of Falling object
Time (s)
Displacem
ent (m)
Average
Velocity
Instantaneou
s Velocity
(m.s-1)
Accelerati
on (m.s-2)
0
0
0
1
5
5
0
10
10
10
2
20
10
20
10
3
45
80
15
20
30
10
125
25
180
30
40
50
60
10
10
10
4
5
6
Terminal velocity
•
•
•
•
•
•
•
Falling objects …………………………….. at
…………………..
The velocity increases every second and the
……………………………… every second
increases as well.
The ……………………………… increases
with every second that the object is falling.
Each particle applies a small force on the
object and the until the ……………………
……………………… to the downward force
of gravity.
There is …………………………. force and
therefore no acceleration.
The object will continue to move at ………….
………………….
This velocity we call ……………………. The
terminal velocity of an object is dependant on
its size and shape.
From World Book © 2002 World Book, Inc., 233 N.
Michigan Avenue, Suite 2000, Chicago, IL 60601.
All rights reserved. World Book illustration by David
Cunningham
Terminal velocity
•
•
•
•
•
•
•
Falling objects initially accelerate downwards
at 9.8m/s2.
The velocity increases every second and the
distance that is covered every second
increases as well.
The number of collisions with air particles
increases with every second that the object is
falling.
Each particle applies a small force on the
object and the until the upward force of all
the collisions is equal to the downward force
of gravity.
There is no longer any resultant force and
therefore no acceleration.
The object will continue to move at constant
velocity.
This velocity we call terminal velocity. The
terminal velocity of an object is dependant on
its size and shape.
From World Book © 2002 World Book, Inc., 233 N.
Michigan Avenue, Suite 2000, Chicago, IL 60601.
All rights reserved. World Book illustration by David
Cunningham
Equations of motion for free fall and vertical
projectile motion
An object is in “……..
……………” if:
• it is moving ….. or
……….. without
……………. other
than ……………
• we ignore ……….
……………..
• we can substitute
“g” for “a” in
equations because
the …………..
………………….
is gravity.
v  u  gt
1 2
s  ut  gt
2
Gravity
2
2
v  u  2 gs
Equations of motion for free fall and vertical
projectile motion
An object is in “free fall”
if:
• it is moving up or
down without
influence other than
gravity
• we ignore air friction
• we can substitute “g”
for “a” in equations
because the only
acceleration is gravity.
Gravitational
Acceleration
9.8 m.s-2
• vf = vi + at
• x = vi t + 1/2a t2
• vf2 = vi2 + 2a x
(vi + vf) t
• x =
2
Gravitation and Falling Bodies
An object is thrown vertically
up into the air and allowed to
fall back down.
V= ……., a = …………
+
Fg = mg
V = (…)
a = ………
• The only force on the
object is its …………….
• The object continually
…………………………….
• Take the upwards as
positive, acceleration
downwards …………….
• Velocity momentarily
……….. at apex.
Fg = mg
• Time up = …………….
V = (….)
• velocity at return = ………
…………………
a = ………..
Gravitation and Falling Bodies
An object is thrown vertically
up into the air and allowed to
fall back down.
V=(0), a =
+
Fg = mg
V = (+)
a = -10m/s2
-10m/s2
• The only force on the
object is its weight.
• The object continually
accelerates downwards.
• Take the upwards as
positive, acceleration
downwards negative.
Fg = mg
V = (-)
a=
-10m/s2
• Velocity momentarily zero
at apex.
• Time up = time down
• velocity at return =
velocity of projection
Sketch graphs – Free fall
Sketch the following graphs for each of the following motions (Ignore
friction):
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
1.
2.
2.
A ball falls freely from rest.
A ball is thrown vertically upward and returns to the throwers hand.
Consider only the period of free fall and take upward direction as
positive (+ve).
A super-ball (Energy conserved) is dropped to the floor and bounces
back to the same height.
A ball falls freely from rest.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
+
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A ball falls freely from rest.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
+
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A ball is thrown vertically upward and returns
to the throwers hand.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
fall and take upward
direction as positive (+ve).
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A ball is thrown vertically upward and returns
to the throwers hand.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
fall and take upward
direction as positive (+ve).
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A super-ball (Energy conserved) is dropped to the floor and
bounces back to the same height.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
+ fall and take downward direction
as - ve.
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A super-ball (Energy conserved) is dropped to the floor and
bounces back to the same height.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
+ fall and take downward direction
as - ve.
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A super-ball (Energy conserved) is dropped to the floor and
bounces back to the same height.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
- fall and take downward direction
as + ve.
s
b)
t
v
s
d)
e)
t
a
c)
t
t
A super-ball (Energy conserved) is dropped to the floor and
bounces back to the same height.
a) velocity vs. time
b) displacement vs. time
c) acceleration vs. time
d) speed vs. time
e) distance vs. time
v
a)
t
Consider only the period of free
- fall and take downward direction
as + ve.
s
b)
t
v
s
d)
e)
t
a
c)
t
t