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5. Universal Laws of Motion
“If I have seen farther than others, it
is because I have stood on the
shoulders of giants.”
Sir Isaac Newton (1642 – 1727)
Physicist
© 2004 Pearson Education Inc., publishing as Addison-Wesley
5.1 Describing Motion: Examples from
Daily Life
Our goals for learning:
• Distinguish between speed, velocity, and
acceleration.
• What is the acceleration of gravity?
• How does the acceleration of gravity depend on
the mass of a falling object?
• How do you know when a net force is acting on
an object?
• Have you ever been weightless? Have you ever
been massless?
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Objects in Motion
• speed – rate at which an object moves, i.e. the
distance traveled per unit time [m/s; mi/hr]
• velocity – an object’s speed in a certain
direction, e.g. “10 m/s moving east”
• acceleration – a change in an object’s velocity,
i.e. a change in either speed or direction is an
acceleration [m/s2]
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Galileo's Famous Experiment
The Acceleration of Gravity
• As objects fall, they
accelerate.
• The acceleration due
to Earth’s gravity is
10 m/s each second,
or g = 10 m/s2.
• The higher you drop
the ball, the greater
its velocity will be at
impact.
© 2004 Pearson Education Inc., publishing as Addison-Wesley
The Acceleration of Gravity (g)
• Galileo demonstrated that g is the same for all objects,
regardless of their mass!
• This was confirmed by the Apollo astronauts on the
Moon, where there is no air resistance.
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Acceleration of Gravity
• Any object which is being
acted upon only by the force
of gravity is said to be in a
state of free fall. There are
two important motion
characteristics which are true
of free-falling objects:
– Free-falling objects do not
encounter air resistance.
– All free-falling objects (on
Earth) accelerate downwards
at a rate of 9.8 m/s/s (often
approximated as 10 m/s/s)
• If the velocity and time for a free-falling object being
dropped from a position of rest were tabulated, then one
would note the following pattern.
• Time (s)
Velocity (m/s)
• 0
0
• 1
- 9.8
• 2
- 19.6
• 3
- 29.4
• 4
- 39.2
• 5
- 49.0
Free Fall
• Newton’s 2nd Law
predicts this!
a=
F
m
• The force of gravity
felt by a more massive
object is greater
Air Resistance
• Air resistance is an upward force exerted on
an object as it falls by air
• It is, in essence, a frictional force
• For simplicity, the amount of air resistance
is determined by two factors
– The cross-sectional area of the object
– The speed of the object
Terminal Velocity
Determine the acceleration of this 85 kg skydiver at points A-D.
(Hint: F=ma)
9.8 m/s2
5.68 m/s2
1.56 m/s2
0 m/s2
Terminal Velocity
• The terminal velocity of a skydiver in a
free-fall position with a semi-closed
parachute is about 195 km/h
• Higher speeds can be attained if the
skydiver pulls in his limbs. In this case, the
terminal velocity increases to about 320
km/h!
• The more compact and dense the object, the higher its terminal
velocity will be. Typical examples are the following: raindrop,
25 ft/s, a skydiver was found to be in a range from 53 m/s to 76 m/s
W Richards Worthing High
School
Terminal Velocity
Consider a skydiver:
1) At the start of his jump the air
zero so he
resistance is _______
____ downwards.
accelerates
2) As his speed increases his air
increase
resistance will _______
3) Eventually the air resistance will be
big enough to _______
balance the
skydiver’s weight. At this point
the forces are balanced so his
constant - this is
speed becomes ________
called TERMINAL VELOCITY
How the forces change with time.
KEY
Gravity
(constant
value & always
present…weight)
Air resistance
(friction)
Net force
(acceleration OR
changing velocity)
Possible Test Questions:
• What factor causes terminal velocity to occur?
• If an object is at terminal velocity, is it speeding
up, slowing down, or falling at a constant speed?
• Describe and explain how forces change on a
falling object.
Forces
• Forces change the motion of objects.
• momentum – the (mass x velocity) of an object
• force – anything that can cause a change in an
object’s momentum
• As long as the object’s mass does not change,
the force causes a change in velocity, or an…
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Momentum
• Momentum is inertia in motion.
It is determined by how big an object is and
how fast it is moving.
p=mxv
(kg x m/s)
A stationary object has zero momentum.
Is Mass the Same Thing as Weight?
• mass – the amount of matter in an object
• weight – a measurement of the force which
acts upon an object
When in “free-fall,”
you are weightless!!
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Projectile Motion
•An object thrown upward at an angle to the
ground follows a curved path called a parabola.
• combines vertical and horizontal motion
•Orbiting objects- forward motion combines with
free fall and object follows a curved path
Projectile Motion
• Projectile: When a
falling object also
experiences
horizontal motion
• Horizontal motion
does not affect
vertical motion
Newton’s Universal Law of
Gravitation
Isaac Newton discovered that it is gravity which
plays the vital role of determining the motion of the
planets - concept of action at a distance
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Newton’s Universal Law of
Gravitation
Between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the
distance between the centers of the objects.
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Newton’s Universal Law of
Gravitation
G=6.67 x 10-11 m3/(kg s2)
© 2004 Pearson Education Inc., publishing as Addison-Wesley
•How does the acceleration of gravity depend on the mass
of a falling object?
•It does not. All falling objects fall with the same
acceleration (on a particular planet).
•Now see why…
•F = ma and on Earth acceleration due to gravity
denoted “g” so F=mg or g=F/m
•If mass of earth is M1 then Fg=GM2/d2
© 2004 Pearson Education Inc., publishing as Addison-Wesley