Download free fall motion

KOLEJ MATRIKULASI LABUAN
PULAU LABUAN
WS011
SAINS INFOMATIK
FREE FALL MOTION
NUM. NAME
MATRIC CARD
COLLEGE
1
SAHLAN BIN ABDUL KADIR
MS0915516533
KOLEJ MATRIKULASI LABUAN
2
ALEX LU CHIA YANG
MS0915545059
KOLEJ MATRIKULASI LABUAN
3
JACKSON BIN KEMBIN
MS0915515231
KOLEJ MATRIKULASI LABUAN
4
NOOR FARIHAH BINTI HAMRIL
MS0915516051
KOLEJ MATRIKULASI LABUAN
5
MIMA AN-NUR BINTI JUNIDAY
MS0915515652
KOLEJ MATRIKULASI LABUAN
NO.
CONTENT
SUB-TOPIC
1.1
INTRODUCTION
1.2
FREE FALL
1.2.1 Definition
1.3
THEORY
1.3.1 Equation For Free Fall
1.3.1.1 Deriving The Equation Of
Motion
1.3.2 How Fast
1.3.3 How Far
1.3.3.1 Difference in Velocity
1..3.3.2 Difference In Distance
1.3.4 Representing a Free Fall
Motion Using Graphs
1.4
Characteristic
Of
Free
Fall
Motion
1.5
Application Of Free Fall Motion
1.6
Problem-Solving
1.7
Conclusion
1.8
Reference
1.1 INTRODUCTION
What is physics concept that can explain the phenomenon of two objects with differents weight
and mass are striking the ground at the same time when they are release at the same height?
Why something thrown upwards at a certain speed will return to its starting point with the same
speed although the objects is now moving in the opposite direction? This is the common
question that will arise when we are discussing the free fall phenomenon.
In this topic, we will study the free fall phenomenon: an object are moving upward and
downward along a straight line vertically. Here, we will discuss the acceleration due to gravity t
hat was affecting the motion of free falling bodies.
An important part of how the free fall motion occur is the acceleration due to gravity. This
physical quantity are parcel in the study of free fall motion. Since, it is the only force that will
be considered greatly in the study of free fall phenomenon.
Note : acceleration due to gravity is represented as g.(g = 9.80 m s-2)
A ping pong ball
direction
of the
motion
g = -(-9.80 m s‾²)
Ground
1.2 FREE FALL
1.2.1 Definition
Free fall according to Paul G. Hewitt are “object in motion solely under the influence of gravity
are said to be in free fall”. The phrase “free fall” illustrate that the dropped object that are
moving
downward under the influence of the gravity (g = 9.80 m s‾² in the absence of air
resistance).
The term can be applied in general to any vertical motion under the sole influence
of
Object released from rest or thrown upward or downward are in free fall state once
they
gravity.
are
release. There are only gravity force is acting and influencing the motion.
Free fall of an object depends on the acceleration for all free-falling object regardless of their
mass or weight. This only happen when distance of the object are not too far from the earth
surface because the acceleration due to gravity are changing with distance of the object from the
earth surface.
For free fall, Galileo has postulated that all object would fall with the same constant
acceleration in the absence of air or other type of resistance. He show that this postulated
predicts that for an object from rest, the distance travelled will be proportional to the square of
the time: That is
d = kt²
d/t2 = k
where k is a constant
A freely falling body are accelerating due to gravity on the earth and we give it the symbol g. Its
magnitude are approximately (9.80 m s2).
NOTE : Its magnitude are 9.80 m s2 only at the surface of the earth
1.3 THEORY
According to Advanced Physics written by Steve Adams and Jonathan Allday, an Appolo
astronauts has conducted an experiment on the moon surface by dropping a hammer and a
feather on the moon surface to shows that all objects are fall with the same acceleration in the
same gravitational field. If the experiment are conducted on earth then we need to remove
resistive force such as air resitance by dropping things inside an evacuated container. During
free fall the resultant force on a body is its own weight.
In vacuum
Figure 1 An experiment carried out in vacuum to remove air resistance
Note : g =gravitational acceleration = 9.80 m s-2
Resultant force
F = mg
Newton's second law
F = ma
mg = ma
a=g
The term of free fall is including dropping as well as upward or downward throwing. Any
objects that falls freely are experiencing an acceleration directed to the center of the earth or
downward, no matter the direction of the initial movement.
Upward = -9.8 m s‾²
Vy = 0
Downward = +9.8 m s‾²
Figure 1 Showing the motion of free-falling ball (a = g = -9.8 m s‾²)
1.3.1 Equation For Free Fall
Since free fall are accelerating constantly, then we can use the equation of motion to
solve the problem under the topic of free fall motion.
s = ½(v - u)t
s = ut + ½at
v = u + at
v2 = u2 + 2as
Since the motion of free fall phenomenon is vertical. The equation are changed into:
sy = ½(vy - uy)t
sy = uyt + ½gyt
vy = uy + gyt
vy2 = uy2 + 2gysy
1.3.1.1 Deriving the equation of motion
v = final velocity, u = v0 = initial velocity, a = acceleration, t = time, s =
displacement
From, a = dv/dt = (v + v0)/t
Rearrange the equation:
a = (v + v0)/t …..... (1)
vav
= distance/time = s/t;
But vav
= ½ (v + v0)
So, s = ½(v + v0)t.........(2)
But from (1)
v = v0 + at
Then substitute the equation (1) into s = ½(v + v0)t
s = ½((v0 + at) + v0)t
s = ½(2v0 + at)t
s = v0t + ½at2..............(3)
From (1)
v = v0 + at
Rearrange equation (1)
t = (v – v0)/a
substitute t into (3)
s = v0t + ½at2
s = v0((v – v0)/a) + ½a(((v-v0)a)(v – v0)/a)))
2as = 2v0v – 2v02 + (v2 - 2v0v + v02)
v2 = v02 + 2as.................(4)
1.3.2 How Fast
Things are falling because of the force of gravity. When a falling objects is free of all
restraint, such as friction and falls under the influence of gravity alone, the object is in a
state of free fall. The instantenous speed or velocity of an objects falling from rest is
consistent with the evaluation that Galileo deduced with his inclined planes:
Velocity acquired, v = acceleration(a) * time(t)
1.3.3 How Far
Here the distance is d = h and the acceleration is that of gravity, so a = g, which gives
h = ½gt2 (object falling from rest). The t2 factor means that h increases with time much
faster than the object's speed v, which is given by v = gt. At t = 10s, the objects speed at
t = 1s, but the distance it has fallen is 100 times the distance it fell during the first
second.
1.3.3.1 Differents in Velocity
At t = 1s
v = (9.80 m s-2)(1s)
v = 9.8 m s-1
At t = 10s
v = (9.80 m s-2)(10s)
v = 98.0 m s-1
velocity at the ten second is ten times greater than in the first second
1.3.3.2 Differents in Distance
At t = 1s
h = ½(9.8 m s-2)(1s)2
h = 4.9 m s-1
At t = 10s
h = ½(9.8 m s-2)(10s)2
h = 490 m s-1
distance travelled after ten second is 100 times greater than the distance in the
first second.
t = 1s, v = 9.80 m s‾¹, h = 4.9 m
t = 10s, V = 98.0 m s‾¹,h = 490 m
Figure 2 The changes of velocity and distance travelled in free fall
1.3.4 Representing a Free Fall Motion Using Graph
There are two basic type of graphs that used to representing the free fall motion;
a). displacement-time graph
Displacement / m
Time / s
b). velocity-time graph
Velocity / m sˉ¹
Time / s
1.4 CHARACTERISTIC OF FREE FALL MOTION
Free falling motion have two important characteristic that:
a). Free falling bodies does not encounter air resistance.
This characteristic is arise because the free falling bodies are only affected by
gravitational force. This characteristic also showing us that the shape, mass,
weight and any other factor are not affecting the motion of free falling bodies. An
object that are in free fall state are experiencing weightlessness.
b).Free falling bodies is accelerating downwards at a rate of approximately 10 m s-2 (to
be exact 9.8 m s-2).
This characteristic are only accepted when the objects are near with the earth.
This is happen because gravitational acceleration reduces with altitude. That was
showing that the farther the distance of the object from the earth, the lower its
value. The gravitational acceleration were assumed to be constant on the earth
surface.
Weak gravitational acceleration
earth
Strong gravitational acceleration
distance
Figure 3 Further object from the earth, lesser gravitational acceleration it's experiencing
1.5 APPLICATION OF FREE FALL
In sport:a). Bungee jumping.
Free fall concept can be seen in bungee jumping by the acceleration of the player
towards earth's center.
b). Sky diving
Free fall concept can be seen in sky diver's by the acceleration of the
player towards earth's center.
1.6 PROBLEM-SOLVING
1). A boy throws a ball up towards the sky. The initial velocity of the ball is 25 m s-1 when it
leaves his hand.
a). What is the maximum height that the ball reaches ?
b). How long does it take to reach the highest point ?
c). What is the position of the ball at t = 1.0s ?
Solution:
a).when maximum height is reached then the value of the velocity is zero.
v = 0 m s-1, u = 25 m s-1, vy2 = u y2 – gysy
0 m s-1 = (25 m s-1)2 - (9.8 m s-2)(sy)
sy = 31.86 m
b). using vy = uy - 2gyt
0 m s-1 = (25 m s-1) – (9.80 m s-2)(t)
t = 2.55 s
c).using sy = uyt – ½gyt2
= (25 m s-1)(1.0 s) - ½(9.80 m s-2)(1.0 s)2
= 20.10 m
2). A stone is thrown vertically upward with a speed of 20 m s-1
a). The position and velocity of the ball after 1 s.
b). The velocity when the ball is 4 m above its initial level.
c). The maximum height and the time required to reach the maximum height.
d). The total time taken to return to its initial level.
Solution
a). sy = uyt – ½gyt2
= (20 m s-1)(1.0 s) - (9.80 m s-2)(1.0 s)
= 15.10 m
vy = uy – gyt
= (20 m s-1 ) - (9.80 m s-2)(1.0 s)
= 10.19 m s-1
b). vy2 = uy2 - 2gysy
v2 = (20 m s-1)2 - 2(9.80 m s-2)(4 m)
= 17.93 m s-1
c). At maximum height v = 0 m s-1
0 m s-1 = (20 m s-1)2 - 2(9.80 m s-2)(s)
s = 20.39 m
using vy = uy – gyt
0 m s-1 = 20 m s-1 - (9.80 m s-2)(t)
t = 2.04 s
d). sy = uyt – ½gyt2
0 m = (20 m s-1)(t) - (9.80 m s-2)(t2)
factorise the equation,
t = 0s, 4.08 s
3). A rock falls from a ledge 10 m above the ground. How fast is it moving just before it hits the
ground?
we know
u = 0 m s-1; s 10 m s-1; a = 9.8 m s-2
we want v. use
vy2 = uy2 – 2gysy
u2 = 0 ms-1 – 2(-9.8 m s-2)(10 m)
u = 14 m s-1
1.7 CONCLUSION
The free fall motion are only occur effectively on the absence of the air resistance and other
factor that able to disrupt the free fall motion. The most accurate measurement for free fall
motion is when it is occur in vacuum. Since, in vacuum there will no air resistance acting on the
object. Not only that, a long range free fall motion will not experience a constant acceleration
due to gravity because the gravitational acceleration are changing with the altitude.
1.8 REFERENCE
1. GLENCOE PHYSICS (PRINCIPLE AND PROBLEMS), PAUL W.ZITZENITZ, Ph. D,
A DIVISION OF THE MC. GRAW. HILL COMPANIES.
2. PHYSICS FOR SCIENTIST AND ENGINEERS WITH MODERN PHYSICS
FOURTH EDITION, SERWAY, SAUNDERS COLLEGE PUBLISHING.
3. CONCEPTUAL PHYSICS NINTH EDITION, PAUL G. HEWITT, LIBRARY OF
CONGRESS CATOLOGY IN PUBLICATION DATA.
4. APPLIED PHYSICS, EIGHT EDITION, DALE EWEN, NEILL SCHURTER, P. ERIK
GUNDASEN, PEARSON (PRENTICE HALL) UPPER SEDDLE RIVER, NEW
JERSEY, COLUMBUS, OHIO.
5. PRE-UNIVERSITY PHYSICS VOLUME 1, NOR SABIRIN MOHAMED, IZLINA
SUPA'AT, NORAZLIN ZAINAL, HASHLINA RUSDI, SHARUL AMIR, U.FERWANI
SALWA
U.
IBRAHIM,
EUGENE
HECHT,
PHYSICS
ALGEBRA
AND
TRIGONOMETRY, 3E, BY EUGENE HECHT.
6.
PHYSICS PRINCIPLE WITH APPLICATION SIXTH EDITION BY DOUGLAS C.
GIANCOLI. PUBISHED BY PEARSON EDUCATION INTERNATIONAL.
7. THE
PHYSICAL
UNIVERSE
ELEVENTH
EDITION
BY
KONRAD
B.
KRAUSKOPT(STANFORD UNIVERSITY) AND ARTHUR BEISER. PUBLISHED
BY MC. GRAW-HILL
8. UNIVERSITY
PHYSICS/HUGH
D.
YOUNG,
ROGER
A.
FREEDMAN;
CONTRIBUTING AUTHORS, T.R. SANDIN, A. LEWIS FORD.
9. ADVANCED PHYSICS/ STEVE ADAMS, JONATHAN ALLDAY.
10. GCSE PHYSICS/ TOM DUNCAN
11. ENCARTA ® WORLD ENGLISH DICTIONARY © 1998 – 2003 MICROSOFT
CORPORATION. ALL RIGHT RESERVED. DEVELOPED FOR MICROSOFT BY
BLOOMSBURY PUBLISHING Plc.
TRANSLATION DICTIONARIES COPYRIGHT C.LANGENSCHEIDT KG BERLIN
AND MUNICH 2000.