Forces, Momentum, & Gravity
(Chapter 3)
Student Learning Objectives
• Recall and apply each of Newton’s Laws.
• Relate momentum to impact force.
• Use conservation of momentum to analyze motion.
• Describe gravity and its applications.
What is a force & when are forces balanced?
 A force is the amount of push or pull on an object.
 Forces can cause a change in motion; a net force
results in acceleration.
Fnet = ∑ F
 An object in mechanical equilibrium maintains
its motion. There is no change.
Fnet = 0
Forces are balanced
Practice
1) If a car engine provides 700 Newtons of push, and
there is 200 Newtons of opposing friction, what is the
net force on the car?
2) When the car engine continues to provide 700
Newtons of push, but the friction force is increased to
700 Newtons, what is the net force on the car? Would
this cause the car to stop?
More Practice
3) Is a car with a constant velocity of 30 mph in
mechanical equilibrium? Why must you keep
pressure on the accelerator?
4) A 150 lb person is standing still on the floor. What is
the net force?
What are Newton’s Laws of Motion?
Newton’s 1st Law of Motion: Inertia
An object will remain at rest or maintain a
constant velocity unless an unbalanced force
causes the object’s motion to change.
 Inertia is the tendency of an object to maintain its motion.
Examples of Inertia
Quick stops
Cornering
Coffee on your dash
The tablecloth trick
http://www.physicsclassroom.com/mmedia/newtlaws/cci.cfm
Mass
Inertia depends on mass.
more mass  more inertia
 harder to change motion
Mass is a fundamental quantity.
Mass is the amount of material contained in an
object.
Empty 747 Jet
Average Man
5¢ coin
160,000 kg
73 kg
0.0052 kg
Practice
Mass is often defined in elementary school as
“the amount of space an object takes up”. Why
is this not correct?
Newton’s 2nd Law of Motion: F = ma
An unbalanced force acting on a mass gives the
mass an acceleration in the same direction as
the unbalanced force.
F = ma
friction
When an object is in
motion, friction is always
in the opposite direction
of the motion.
Big
Box
Normal Force
The normal force is
perpendicular to the
surface.
FN
Motion
Ff
Support Force
Practice
1) If the force on a 5 kg mass is tripled, what will
happen to the rate of acceleration?
2) A 2000 kg car engine provides 9800 N of push
southward. The opposing frictional force is
1200 N. What is the average acceleration?
Weight
Weight is a force.
Weight is the gravitational force acting on a
mass.
W = mg
On Earth, 1 kg of mass weighs 9.8 Newtons or
2.2 pounds.
Practice
1) Does weight depend on volume?
2) Would 1 kg of mass weigh 2.2 pounds on the Moon?
3) If you were instantly transported to Mars, which
would change:
Mass? Weight? Inertia?
More Practice
4) A person weighs150 lb (667 N) on Earth.
a) What is the mass of this person?
b) What would a person weigh on Mars? The
acceleration due to gravity on Mars is 3.72 m/s2.
Vectors
 Forces are vectors, and vector addition is the addition of
both the size and direction of each quantity.
http://www.physicsclassroom.com/mmedia/vectors/rb.cfm
http://www.physicsclassroom.com/mmedia/vectors/plane.cfm
 The resultant vector shows the result of two or more
vectors acting simultaneously.
Practice
An airplane’s speedometer reads 500 mph North.
What is the net velocity of the airplane in each
case?
a) Wind is blowing North at 50 mph.
b) Wind is blowing South at 50 mph.
c) Wind is blowing East at 50 mph.
Newton’s 3rd Law of Motion: Action-Reaction
When two objects interact, they create equal and
opposite forces on each other.
F1 = −F2
 To every action force there is an equal (in magnitude) and
opposite (in direction) reaction force when two objects
are in contact.
Pushing on a Wall
Bat & Ball
Rockets
Space X
Practice
If I give the chair a good push, it goes from rest
to having a velocity, and then stops. How do
each of Newton’s laws apply to this system?
What is momentum?
Linear momentum is the The greater the
combination of mass
momentum, the harder it
(inertia) and velocity.
is to stop an object!
p = mv
Practice
1) What is an example of a moving object that
could have a large momentum because it has a
large mass?
2) What is an example of a small object that
could have a large momentum because it has a
large velocity?
More Practice
3) Which has the most momentum?
a) 10,000 lb (4535 kg) 18-wheeler parked at the curb
b) 300 lb (136 kg) football player running 10 mph (4.46 m/s)
c) 150 lb (68 kg) sprinter running 22 mph (9.83 m/s)
d) 1200 kg car moving at 1 m/s
Angular momentum is momentum in a circular
path.
L = mvr
 The angular momentum vector is perpendicular to the
plane of the circular path.
L
v
http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html
How does momentum affect the force of impact?
During an impact, the force of impact depends on
how quickly the momentum is changed.
F = Dp
t
Barrels & Divided Highway
Carpet vs. Concrete
Practice
1) What are some features of car design that decrease
force of impact?
2) You (75 kg) are riding in your 2000 kg car at 30 m/s
(67 mph) when suddenly a squirrel runs in front of
you; you swerve, and hit a tree. If the duration of
the impact is 1/2 of a second, what is the impact
force?
More Practice
3) Two 2000 kg cars, each with a 75 kg person, are
traveling toward each other with a speed of 30 m/s
(67 mph); suddenly one swerves into the wrong lane
and there is a head-on collision. If the duration of the
impact is 1/2 of a second, what is the impact force on
each car?
How is conservation of momentum applied?
The total momentum of an isolated system remains
constant.
pf = pi
Lf = Li
Collisions & Ice Skaters
http://www.physicsclassroom.com/mmedia/momentum
Practice
1)Two cars of equal mass collide. One is traveling West at
30 m/s, the other is at rest. Then there is an inelastic
collision between the two cars. If linear momentum is
conserved, what is the final velocity of each car?
2) An ice skater spins 5 m/s with outstretched arms. The
radius of the circular path traced by her arms is 1 meter.
Then she pulls her arms in, changing the radius of the
circular path to 1/3 m. If angular momentum is
conserved, what is her new spinning speed?
What is Newton’s description of gravity?
 Newton’s Universal Law of Gravitation
Every object with mass attracts every other object with
mass, with a force that depends directly on the masses of
the two objects and decreases with the distance squared.
Fg = GMm
d2
Gravity
Mutual force of attraction
All masses pull the same on each other!
Causes acceleration due to gravity
g = 9.81 m/s2
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html
Practice
1) Would the acceleration due to gravity (9.81 m/s2) be
different for an object dropped from a high mountain
top than it is at sea level?
2) If Earth had twice as much mass, would this change
our weight? Would it change our mass?
3) How would the gravitational force change if the
distance doubled?
More Practice
4) What is the gravitational attraction between Earth and
a 75 kg person standing on the surface, at sea level
(ME = 6 x 1024 kg, rE = 6.4 x 106 m)? What do we
normally call this?
5) Is the gravitational force zero in space?
What are some effects of gravity?
The feeling of weightlessness occurs when an
object and its reference frame accelerate at the
same rate.
Airplane drops
Large “dip” in the road
Freefall ride
 If there is no support force, then objects will fall together.
Practice
If you were standing on a bathroom scale in the
elevator, how would the reading change as the elevator
a) Accelerates up
b) Accelerates down
c) Free falls
Gravitational Effects
Gravity is a Universal Force
Orbits
Atmospheres
Tides
Our Earth-Moon system is changing.
 Earth’s rotation is slowing (0.0015 seconds/century)
 Our Moon is drifting away (3.8 cm/year)
 The synchronous orbit of the Moon (same face)
Practice
The Sun's tidal affects are weak compared
to the Moon. Why?
What is Einstein’s description of Gravity?
Every object with mass creates a
curvature of space-time.
 According to Einstein, mass does not create a force, but
rather a warping of space which other objects follow.
 Objects fall independent of their mass because they all
follow the same path in curved space-time.
More Mass = More Curvature