Newton’s 2nd Law of Motion
F=ma
• F = force
– Measured in newtons (N)
• m = mass
units
– Measured in kilograms (kg)
• a = acceleration
– Measured in meters per second
per second (m/s²)
Multiple
forces can
be exerted
on an
object at
the same
time
• acceleration = change in
velocity over time
What is
acceleration
?
a=
𝑣2 − 𝑣1
𝑡
or a =
Δ𝑣
𝑡
Thinking
about
the law
• If the force acting on an
object goes down, and the
mass doesn’t change, how
does the acceleration
change?
• Fg = mag
(or W=mg or F = mg)
Weight is
applied
Newton’s
2nd
– Fg = force due to gravity ( or
W=weight)
– ag (or g) = acceleration due
to gravity
• always = 9.8 m/s2 on Earth
• Does a big guy or little guy fall
faster when bungee jumping?
• Fg = mag
(or W=mg or F = mg)
Weight is
applied
Newton’s
2nd
– Fg = force due to gravity ( or
W=weight)
– ag (or g) = acceleration due
to gravity
• always = 9.8 m/s2 on Earth
• Does a big guy or little guy fall
faster when bungee jumping?
• They fall at the same speed,
as mass is irrelevant to
freefall speed
Free-fall utilizes “g”
The acceleration of
gravity (g) for objects
in free fall at the
earth's surface is 9.8
m/s2.
Galileo found that all
things fall at the same
rate.
Free-fall
The rate of falling
increases by 9.8 m/s
every second.
Height = ½ gt2
(Height is abbreviated either “y” or “d”)
For example:
½ (9.8 )12 = 4.9 m
½(9.8)22 = 19.6 m
½ (9.8)32 = 44.1 m
½ (9.8)42 = 78.4 m
Free-fall
A ball thrown horizontally
will fall at the same rate
as a ball dropped
directly.
Free-fall
A ball thrown into the air
will slow down, stop, and
then begin to fall with the
acceleration due to
gravity. When it passes
the thrower, it will be
traveling at the same rate
at which it was thrown.
Projectile motion path shape
An object thrown upward at an angle to the ground follows a
curved path called a parabola.
What do you notice about this shape?
Air Resistance and free-fall
• In air…
– A stone falls faster than a
feather
• Air resistance
affects stone less
• In a vacuum
– A stone and a feather will fall
at the same speed.
Air Resistance and free-fall
– A person in free fall
reaches a terminal
velocity of around 54 m/s
(about 130 mi./hr.)
– With a parachute, terminal
velocity is only 6.3 m/s
Allows for a safe landing
-the terminal velocity for a
cat is 60 mi./hr.
Air Resistance
•
Ideal angle for a projectile
– In a vacuum, maximum distance is at an angle of 45o
– With air resistance (real world), angle is less
• Baseball will go furthest hit at an angle of around 40o