Forces, Momentum, & Gravity
(Chapter 3)
Student Learning Outcomes: 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.
1. What is a force & when are forces balanced?
2. What are Newton’s Laws of Motion & how do they apply?
3. What is momentum?
4. How does momentum affect the force of impact?
5. How is conservation of momentum applied?
6. What is Newton’s description of Gravity
7. What are some effects of gravity?
8. What is Einstein’s description of Gravity?
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.
An object in mechanical equilibrium maintains its motion. There is no
change.
Fnet = 0
Forces are balanced
Practice:
1) If car engine provides 700 Newtons of push, and there is 200 Newtons of
opposing friction, what is the net force on the car?
Fnet = ∑ FForces, Momentum, Gravity C3 2
2) If car engine provides 700 Newtons of push, and there is 700 Newtons of
opposing friction, what is the net force on the car? Would this cause the car to
stop?
3) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why
must you keep pressure on the accelerator?
What are Newton’s Laws of Motion & how do they apply?
All objects have the same motion within a specific reference frame.
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.
Quick stops
Cornering
Something sliding across your dash as you turn
The tablecloth trick
http://www.physicsclassroom.com/mmedia/newtlaws/cci.cfm
https://www.youtube.com/watch?v=d7iYZPp2zYY
Inertia depends on mass.
Mass is the amount of material contained in an object.
Mass is a fundamental quantity.
Question: Mass is often defined in elementary school as “the amount of space an
object takes up”. Why is this not correct?
Momentum, Gravity C3 3
more mass more inertia harder to change motionForces,
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.
Example: Soccer ball
http://www.grc.nasa.gov/WWW/k-12/airplane/socforce.html
When an object is in motion, friction is always in the opposite direction of
the motion.
Motion
Ff
Practice:
1) Constant velocity = acceleration or no acceleration?
2) If the force on a 5 kg mass is tripled, what will happen to the rate of
acceleration?
3) A 2000 kg car engine provides 9800 N of push southward. The opposing
frictional force is 1200 N. What is the average acceleration?
Weight is a force; it is the gravitational force acting on a mass.
1 kg of mass weighs 9.8 Newtons or 2.2 pounds on Earth.
Practice:
1) Does weight depend on volume?
2) Would 1 kg of mass weigh 2.2 pounds on the Moon?
1 N = 1 kg m/s2 Fnet = ma
W = mg 1 Newton = 0.2248 lb
Big
BoxForces, Momentum, Gravity C3 4
3) If you were instantly transported to Mars, what would change?
Mass? Weight? Inertia?
4) What would a person weigh on Mars if the person weighs150 lb (667 N) on
Earth? The acceleration due to gravity on Mars is 3.72 m/s2
.
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.
To every action force there is an equal (in magnitude) and opposite (in
direction) reaction force when two objects are in contact.
F1 = − F2Forces, Momentum, Gravity C3 5
Examples: Pushing on a wall, Bat & Ball, Rockets
http://www.wimp.com/golfball/
http://www.space.com/25597-spacex-reusable-rocket-falcon9r-video.html
Practice: If I give the chair a good push, it goes from rest to having a velocity, and
then stops. How can we apply each of Newton’s laws to this system?
What is momentum?
Linear momentum is the combination of mass (inertia) and velocity.
The greater the momentum, the harder it is to stop an object!
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?
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.
p = mv kg m/s
L = mvrForces, Momentum, Gravity C3 6
The angular momentum vector is perpendicular to the plane of the circular
path.
L
direction of circular velocity
http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html
http://www.youtube.com/watch?v=8H98BgRzpOM
How does momentum affect the force of impact?
https://www.youtube.com/watch?v=qLp6qH1Izxw
During an impact, the force of impact depends on how quickly the
momentum is changed.
If you want to decrease the force of impact, you must somehow increase the
duration of the impact.
Water barrels at the start of a divided highway
Carpet vs. concrete
Practice:
1) 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?
2) 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?
3) What are some features of car design that decrease force of impact?
F = p
tForces, Momentum, Gravity C3 7
How is conservation of momentum applied?
The total momentum of an isolated system remains constant.
pf = pi Lf = Li
Examples: Collisions & Ice Skaters
http://www.physicsclassroom.com/mmedia/momentum
http://www.youtube.com/watch?v=WSg28pzVXjs
https://www.youtube.com/watch?v=AQLtcEAG9v0
Practice: (Always assume momentum is conserved)
1) If the mass of a system is doubled, what must happen to the velocity when linear
momentum is conserved?
2) 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?
3) 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.
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html
Fg = GMm
d2orces, Momentum, Gravity C3 8
Mutual force of attraction
All masses pull the same on each other!
Causes acceleration due to gravity, g = 9.81 m/s2
Gravitational force decreases rapidly with distance.
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) 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?
4) How would the gravitational force change if the distance doubled?
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, rolling “dip” in the road
Freefall ride
If there is no support force, then objects will fall together.
Practice: If you were standing on a scale in the elevator that measured your
weight, how would the scale reading change as the elevator
a) Accelerates up
b) Accelerates down
c) Free falls orces, Momentum, Gravity C3 9
Gravity is a universal force.
1. Objects orbit
2. Ocean tides
3. Changing Earth-Moon system
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)
4. Atmospheres
Practice: The Sun's tidal affects are weak compared to the Moon. Why?
What is Einstein’s description of Gravity?
https://www.youtube.com/watch?v=LoaOHvy5AcA
https://www.youtube.com/watch?v=JZWyAVN970c
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.
(Chapter 3)
Student Learning Outcomes: 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.
1. What is a force & when are forces balanced?
2. What are Newton’s Laws of Motion & how do they apply?
3. What is momentum?
4. How does momentum affect the force of impact?
5. How is conservation of momentum applied?
6. What is Newton’s description of Gravity
7. What are some effects of gravity?
8. What is Einstein’s description of Gravity?
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.
An object in mechanical equilibrium maintains its motion. There is no
change.
Fnet = 0
Forces are balanced
Practice:
1) If car engine provides 700 Newtons of push, and there is 200 Newtons of
opposing friction, what is the net force on the car?
Fnet = ∑ FForces, Momentum, Gravity C3 2
2) If car engine provides 700 Newtons of push, and there is 700 Newtons of
opposing friction, what is the net force on the car? Would this cause the car to
stop?
3) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why
must you keep pressure on the accelerator?
What are Newton’s Laws of Motion & how do they apply?
All objects have the same motion within a specific reference frame.
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.
Quick stops
Cornering
Something sliding across your dash as you turn
The tablecloth trick
http://www.physicsclassroom.com/mmedia/newtlaws/cci.cfm
https://www.youtube.com/watch?v=d7iYZPp2zYY
Inertia depends on mass.
Mass is the amount of material contained in an object.
Mass is a fundamental quantity.
Question: Mass is often defined in elementary school as “the amount of space an
object takes up”. Why is this not correct?
Momentum, Gravity C3 3
more mass more inertia harder to change motionForces,
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.
Example: Soccer ball
http://www.grc.nasa.gov/WWW/k-12/airplane/socforce.html
When an object is in motion, friction is always in the opposite direction of
the motion.
Motion
Ff
Practice:
1) Constant velocity = acceleration or no acceleration?
2) If the force on a 5 kg mass is tripled, what will happen to the rate of
acceleration?
3) A 2000 kg car engine provides 9800 N of push southward. The opposing
frictional force is 1200 N. What is the average acceleration?
Weight is a force; it is the gravitational force acting on a mass.
1 kg of mass weighs 9.8 Newtons or 2.2 pounds on Earth.
Practice:
1) Does weight depend on volume?
2) Would 1 kg of mass weigh 2.2 pounds on the Moon?
1 N = 1 kg m/s2 Fnet = ma
W = mg 1 Newton = 0.2248 lb
Big
BoxForces, Momentum, Gravity C3 4
3) If you were instantly transported to Mars, what would change?
Mass? Weight? Inertia?
4) What would a person weigh on Mars if the person weighs150 lb (667 N) on
Earth? The acceleration due to gravity on Mars is 3.72 m/s2
.
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.
To every action force there is an equal (in magnitude) and opposite (in
direction) reaction force when two objects are in contact.
F1 = − F2Forces, Momentum, Gravity C3 5
Examples: Pushing on a wall, Bat & Ball, Rockets
http://www.wimp.com/golfball/
http://www.space.com/25597-spacex-reusable-rocket-falcon9r-video.html
Practice: If I give the chair a good push, it goes from rest to having a velocity, and
then stops. How can we apply each of Newton’s laws to this system?
What is momentum?
Linear momentum is the combination of mass (inertia) and velocity.
The greater the momentum, the harder it is to stop an object!
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?
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.
p = mv kg m/s
L = mvrForces, Momentum, Gravity C3 6
The angular momentum vector is perpendicular to the plane of the circular
path.
L
direction of circular velocity
http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html
http://www.youtube.com/watch?v=8H98BgRzpOM
How does momentum affect the force of impact?
https://www.youtube.com/watch?v=qLp6qH1Izxw
During an impact, the force of impact depends on how quickly the
momentum is changed.
If you want to decrease the force of impact, you must somehow increase the
duration of the impact.
Water barrels at the start of a divided highway
Carpet vs. concrete
Practice:
1) 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?
2) 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?
3) What are some features of car design that decrease force of impact?
F = p
tForces, Momentum, Gravity C3 7
How is conservation of momentum applied?
The total momentum of an isolated system remains constant.
pf = pi Lf = Li
Examples: Collisions & Ice Skaters
http://www.physicsclassroom.com/mmedia/momentum
http://www.youtube.com/watch?v=WSg28pzVXjs
https://www.youtube.com/watch?v=AQLtcEAG9v0
Practice: (Always assume momentum is conserved)
1) If the mass of a system is doubled, what must happen to the velocity when linear
momentum is conserved?
2) 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?
3) 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.
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html
Fg = GMm
d2orces, Momentum, Gravity C3 8
Mutual force of attraction
All masses pull the same on each other!
Causes acceleration due to gravity, g = 9.81 m/s2
Gravitational force decreases rapidly with distance.
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) 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?
4) How would the gravitational force change if the distance doubled?
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, rolling “dip” in the road
Freefall ride
If there is no support force, then objects will fall together.
Practice: If you were standing on a scale in the elevator that measured your
weight, how would the scale reading change as the elevator
a) Accelerates up
b) Accelerates down
c) Free falls orces, Momentum, Gravity C3 9
Gravity is a universal force.
1. Objects orbit
2. Ocean tides
3. Changing Earth-Moon system
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)
4. Atmospheres
Practice: The Sun's tidal affects are weak compared to the Moon. Why?
What is Einstein’s description of Gravity?
https://www.youtube.com/watch?v=LoaOHvy5AcA
https://www.youtube.com/watch?v=JZWyAVN970c
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.