Inertia
• Inertia: The tendency of an object to resist change in motion
– Hammer and Lead
– Feather
• Mass: Our measure of inertia
To get an object to move, or to change its motion,
you must overcome its inertia.
Apply some force.
Newton’s 1st Law
An object at rest, remains at rest,
Newton’s 1st Law
An object at rest, remains at rest,
OR
if in motion, travels in a straight line at constant velocity,
Newton’s 1st Law
An object at rest, remains at rest,
OR
if in motion, travels in a straight line at constant velocity,
UNLESS
acted on by a net force.
Newton’s 1st Law
An object at rest, remains at rest,
OR
if in motion, travels in a straight line at constant velocity,
UNLESS
acted on by a net force.
Inertia can be overcome only by the application of a force.
Force on a mass results in a change in velocity (acceleration).
Force is a “net” force.
Net Force
When forces balance, there is equilibrium.
F1
F2
Bo
Diddley
F1 = Force felt by Bo because of Diddley.
F2 = Force felt by Diddley because of Bo.
F1 = F2
Equilibrium
When forces balance, there is equilibrium.
F1
F2
Bo
Diddley
F1 = Force felt by Bo because of Diddley.
F2 = Force felt by Diddley because of Bo.
F1 = F2
Net Force = Acceleration of Mass
F1
Dude
F2
Diddley
F1 = Force felt by Dude because of Diddley.
F2 = Force felt by Diddley because of Dude.
Net Force F = F1+ F2
Fnet
Net Force = Acceleration of Mass
Dude pushes Diddley
F1
Dude
F2
Diddley
Fnet
Net Force = Acceleration of Mass
Dude pushes Diddley, because Diddley is Piddley.
?
!
Dude
Diddley
Fnet
Newton’s 2nd Law
• Acceleration is proportional to the Net Force.
– As the force increases, the acceleration increases
– Triple the force, triple the acceleration
– Without a net force, there is no acceleration and the
object is in equilibrium (if at rest), or the object remains
in motion at a constant velocity moving in a straight line
in accordance with the 1st Law.
• Acceleration varies inversely with the Mass.
– As mass increases, the acceleration decreases
– As mass increases, the greater the force needed to keep
acceleration the same.
Newton’s 2nd Law
• Acceleration is proportional to the Net Force.
• Acceleration is varies inversely with the Mass.
a = F/m
• Force = mass  acceleration
F=ma
Things That Make You Go…Hmmmm.
Straight Line Answer
An object at rest, remains at rest, OR
if in motion, travels in a straight line at constant velocity,
UNLESS acted on by a net force.
Frictional Forces
Frictional Forces act opposite motion and oppose motion.
Frictional Forces are usually proportional to velocity.
F
f
To get the object to move, you must overcome friction.
If F < f, the object sits. If F > f, then there is acceleration
with a Net Force = F-f.
Fnet = m a
F
f
Fnet = Net Force = F - f
F-f=ma
Acceleration
F
f
F-f=ma
a = (F - f )/m
Acceleration
• A 2 kg mass is acted on by a 2 N force. What is its
acceleration?
F=ma
a = F/m
Acceleration
• A 2 kg mass is acted on by a 2 N force. What is its
acceleration?
F=ma
a = 2 N / 2 kg
= 1 m/s2
a = F/m
Acceleration
• A 2 kg mass is acted on by a 2 N force. What is its
acceleration?
a = 2 N / 2 kg
= 1 m/s2
• What if a 1/2 N frictional force was also in place?
F-f = m a
a = (F-f)/m
Acceleration
• A 2 kg mass is acted on by a 2 N force. What is its
acceleration?
a = 2 N / 2 kg
= 1 m/s2
• What if a 1/2 N frictional force was also in place?
a = (2 - 0.5 N)/2 kg
= 0.75 m/s2
F-f = m a
a = (F-f)/m
Newton’s 3rd Law
• For every action there is an equal and opposite reaction.
– Objects can not act on one another without being acted
upon.
– When you strike a wall, does it hurt your hand? You
might say the wall struck you. Newton would say the
force you applied to the wall was the same as that which
the wall applied to you. The wall is bigger and more
massive, therefore has more inertia and was not harmed
as much as you.
Action-Reaction
Action-Reaction
Action-Reaction
Force on Rock from Earth =
Force on Earth from Ball
a
= F/m = g Rock acceleration
a=
F/
m
Earth’s acceleration
Acceleration of Gravity
Things that fall, accelerate at
9.8 m/sec/sec near the
Earth's surface.
This means velocity of a falling
body increases by 9.8 m/sec with
each passing second.
Acceleration is the
change in velocity over the
change in time.
a = Dv/Dt
Mass No Matter
Lead and wood balls accelerate at the same rate when
dropped from Pisa’s leaning tower.
A hammer and feather fall at same rate in a vacuum.
Apollo 15 astronauts tested Galileo's hypothesis on the Moon.
Astronaut David R. Scott, Apollo 15 commander, watches a
geological hammer and a
feather hit the lunar surface
simultaneously in a test of
Galileo's law of
motion concerning falling
bodies.
H-ITT Question
• Newton’s first law of motion says:
A. Force = mass  acceleration
B. You have the right to remain silent.
C. An object at rest, remains at rest, if in motion, travels in a
straight line at constant velocity, unless acted on by a net force.
D. For every action there is an equal and opposite reaction.
E. none of these
H-ITT Question
• Newton’s second law of motion says:
A. Force = mass  acceleration
B. You have the right to remain silent.
C. An object at rest, remains at rest, if in motion, travels in a
straight line at constant velocity, unless acted on by a net force.
D. For every action there is an equal and opposite reaction.
E. none of these
H-ITT Question
• Newton’s third law of motion says:
A. Force = mass  acceleration
B. You have the right to remain silent.
C. An object at rest, remains at rest, if in motion, travels in a
straight line at constant velocity, unless acted on by a net force.
D. For every action there is an equal and opposite reaction.
E. none of these
H-ITT Question
• A 10 kg mass is acted on by a 2 N force. What is its acceleration?
A. 0.2 m/s2
B. 5 m/s2
a = F/m = 2N / 10 kg = 0.2 m/s2
C. 20 m/s2
D. 9.8 m/s2
E. none of these
• A 3 kg mass accelerates by 5 m/s2 due to a force acting on it.
What is the magnitude of the force?
A. 1.66 N
B. 7 N
F = ma = 3 kg 5 m/s2= 15 n
C. 15 N
D. 0.6 N
E. none of these
H-ITT Question
• A constant net force of 1500 N gives a rocket an
acceleration of 2.5 m/s2. What is the mass of the rocket?
A. 3000 kg
B. 10000 kg
2 = 600 kg
m
=
F/a
=
1500
N/
2.5
m/s
C. 1.667 x 10-3 kg
D. 600 kg
E. none of these
Weight and Force
Our weight (W) is an example
of the force (F) we feel due to
the acceleration of gravity (g).
W = mg
(F = ma)
Apparent Weight
W = mg
W = m(g+a)
W = m(g-a)
Weightless
Newton's Law of Universal Gravitation
Fgravity = m GM/R2
This means that the force of gravity between any
two bodies in the universe is equal to a constant
(the Gravitational Constant, G=6.67x10-11 N-m2/kg2)
times the product of the masses of the two bodies in
question (m and M),
divided by the square of the distance between their
centers (R).
Newton's Law of Universal Gravitation
Fgravity = m GM/R2
Double the mass, double the force.
Double the distance, reduce the force by 1/4.
Triple both mass and distance?
Newton's Law of Universal Gravitation
Fgravity = m GM/R2
Double the mass, double the force.
Double the distance, reduce the force by 1/4.
Triple both mass and distance?
3 from M, (1/9) from R2 = Reduce the force by 1/3.
What Goes Up, Must Come Down
Equating Newton's second law with gravity
F=ma
F = m GM/R2
m a = m GM/R2
m = apple, or
m = human, or
m = projectile, or
m = moon?
What Goes Up, Must Come Down
Equating Newton's second law with gravity
F=ma
F = m GM/R2
m a = m GM/R2
a = GM/R2
Acceleration is GM/R2 ,
irregardless of the
mass m.
Gee, its “g”
• g = 9.8 m/s2
• Surface Gravity
BUT, note that it is
dependent on r. Near
the surface r = Rearth
Want to lose weight?
Hike to the top of a
hill. Acceleration due
to gravity will be less,
therefore your weight
will be less.
m
M
r
F = m GM/r2
GM/r2 = g
Force ~ 1/Distance2
• Twice as far away means 1/4 the force
Moon Gravity
• Moon’s Surface Gravity gmoon = G Mmoon/Rmoon2
gmoon = 1.6 m/s/s
Weight on the moon, W = mgmoon
Since gmoon/gearth = 1/6, Wmoon/Wearth = 1/6
• You will weigh 1/6 as much, but your mass on the
moon is the same as mass on the earth! The force
you feel is different on that mass.
Horizontal and Vertical Motion
Projectiles
• Galileo’s Trajectories
x = vox t
y = voy t - 1/2 g t2
The horizontal distance (x)
is just due to the initial
velocity in the horizontal
direction (vox).
Or, how much
energy is imparted to the
object.
Projectiles
x = vox t
y = voy t - 1/2 g t2
Trajectory Modified By Gravity
x = vox t
y = voy t - 1/2 g t2
Path in the absence of g
1/2 g t2
1/2 g t2
Velocities
x = vox t
y = voy t - 1/2 g t2
At the peak, its vertical velocity is zero.
Projectile Range
x = vox t
y = voy t - 1/2 g t2
A projectile is fired!
With vox = 10 m/s and voy = 20 m/s, how high will it go?
How far down range?
Projectile Range
x = vox t
y = voy t - 1/2 g t2
y
vx = vox + axt
vy = voy - g t
x
Equations of motion:
ax = 0
ay = g
x = 10 t
y = 20 t - 5 t2
x and vx for horizontal
y and vy for vertical
vox = 10 m/s
voy = 20 m/s
vx = 10
vy = 20 - 10 t
Projectile Range
x = 10 t
y = 20 t - 5 t2
y
vx = 10
vy = 20 - 10 t
x
t
0
1
2
3
4
vx
10
10
10
10
10
x
0
10
20
30
40
vy
20
10
0
-10
-20
y
0
15
20
15
0
max height
hits ground
Traveled 40 meters down range and 20 meters high in 4
seconds.
Projectile Range
x = 10 t
y = 20 t - 5 t2
y
vx = 10
vy = 20 - 10 t
x
t
0
1
2
3
4
vx
10
10
10
10
10
x
0
10
20
30
40
vy
20
10
0
-10
-20
y
0
15
20
15
0
max height
hits ground
Traveled 40 meters down range and 20 meters high in 4
seconds.
Projectile Range
x = 10 t
y = 20 t - 5 t2
y
vx = 10
vy = 20 - 10 t
x
t
0
1
2
3
4
vx
10
10
10
10
10
x
0
10
20
30
40
vy
20
10
0
-10
-20
y
0
15
20
15
0
max height
hits ground
Traveled 40 meters down range and 20 meters high in 4
seconds.
Projectile Range
x = 10 t
y = 20 t - 5 t2
y
vx = 10
vy = 20 - 10 t
x
t
0
1
2
3
4
vx
10
10
10
10
10
x
0
10
20
30
40
vy
20
10
0
-10
-20
y
0
15
20
15
0
max height
hits ground
Traveled 40 meters down range and 20 meters high in 4
seconds.
Projectile Range
x = 10 t
y = 20 t - 5 t2
y
vx = 10
vy = 20 - 10 t
x
t
0
1
2
3
4
vx
10
10
10
10
10
x
0
10
20
30
40
vy
20
10
0
-10
-20
y
0
15
20
15
0
max height
hits ground
Traveled 40 meters down range and 20 meters high in 4
seconds.
Survivor Care Package Drop
How far away must the plane be,
to drop the supplies to the camp if it is
travelling 200 km/hr at an altitude of
1000 meters?
x = vox t
y = voy t - 1/2 g t2
y
x
Survivor Care Package Drop
x=?
y = 1000 meters
vox = 200 km/hr
voy = 0
x = vox t
y = voy t - 1/2 g t2
Survivor Care Package Drop
x = 200 t
1000 = 1/2 g t2
Need t.
t is the amount of time the package takes to go from
the height of the plane to the ground, accelerating at
g but starting from rest.
2000 = 10 t2
200 = t = 14.1 seconds
Survivor Care Package Drop
x = 200 t
1000 = 1/2 g t2
Need time (t).
t is the amount of time the package takes to go from
the height of the plane to the ground, accelerating at
g but starting from rest.
2000 = 10 t2
200 = t = 14.1 seconds
Therefore x = 200 (14.1)
= 2820 meters
Curvature and Force
Centripetal Acceleration
a = v2/r
Centripetal Force
=ma
= m v2/r
Since velocity is a vector, even an object with constant
speed that does not travel in a straight line, must
experience an acceleration since acceleration is a
change in velocity. Velocity is a vector which
includes speed AND direction. Therefore, acceleration is a
changing speed or changing direction.
Gravity Works Everywhere
Newton’s Orbit Cannon
• How much Velocity is Required?
Summary
• Newton’s Laws of Motion
– Inertia
– F = ma
– Action/Reaction
• Forces, Acceleration and Equilibrium
• Gravity
F = m GM/r2
x = vox t
• Projectiles
y = voy t - 1/2 g t2