1. Forces, Momentum, & Gravity
(Chapter 3)

2. Force and Motion – Cause and Effect
In chapter 2 we studied motion but not its cause.
In this chapter we will look at both force and motion – the cause and effect.
We will consider Newton’s:
Newton’s three laws of motion
Newton’s law of universal gravitation
Buoyancy and momentum
Intro

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.

4. Sir Isaac Newton (1642 – 1727)
Only 25 when he formulated most of his discoveries in math and physics
His book Mathematical Principles of Natural Philosophy is considered to be the most important publication in the history of Physics.
Intro

5. 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
Fnet = ∑ F

6. Balanced (equal) forces, therefore no motion.
Equal in magnitude but in opposite directions.
Section 3.1

7. Unbalanced forces result in motion
Net force to the right
Section 3.1

8. Practice
1) A 150 lb person is standing still on the floor. What is the net force? 2) 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? 3) 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? 4) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why must you keep pressure on the accelerator?
700N-200N=500N
Net Force would be equal to zero. No, it stop speeding up or slowing down.
You need to overcome the friction

9. 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

10. A spacecraft keeps going because no forces act to stop it
Photo Source: Copyright © Bobby H. Bammel. All rights reserved.
Section 3.2

11. Photo Source: Copyright © Bobby H. Bammel. All rights reserved.
A large rock in Yellowstone N.P. stays put until a large enough force acts on it.
Photo Source: Copyright © Bobby H. Bammel. All rights reserved.
Section 3.2

12. more mass  more inertia  harder to change motion
Crash test with and without safety belt
Mass
Inertia depends on mass.
Mass is the amount of material contained in an object.
Mass is a fundamental quantity.
more mass  more inertia  harder to change motion
Empty 747 Jet
160,000 kg
Average Man
73 kg
5¢ coin kg

13. Mass and Inertia
The large man has more inertia – more force is necessary to start him swinging and also to stop him – due to his greater inertia
Section 3.2

14. Mass and Inertia
Quickly pull the paper and the stack of quarters tend to stay in place due to inertia.
Section 3.2

15. Practice: Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct?
That would be volume.
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
F = ma
Balanced and Unbalanced Forces of a Kicking a Soccer Ball

16. Force, Mass, Acceleration
a a F m
Original situation
If we double the force we double the acceleration.
If we double the mass we half the acceleration.
Section 3.3

17. When an object is in motion, friction is always in the opposite direction of the motion.
Big
Box
Motion Ff
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?
F=ma so 3F would require the acceleration to become 3a since the mass is constant.
9800𝑁−1200𝑁=𝑚𝑎
8600𝑁= 2000𝑘𝑔 𝑎
𝑎=4.3 𝑚 𝑠 2

18. Practice
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.
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, what would change?
a. Mass? b. Weight? c. 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.
No, mass and gravity.
W = mg
No, the moon has less gravity than Earth
𝑥= 𝑚 𝑠 𝑙𝑏 𝑚 𝑠 2 =56𝑙𝑏
𝑥 3.72 𝑚 𝑠 2 = 150𝑙𝑏 9.81 𝑚 𝑠 2

19. Vectors
Forces are vectors, and vector addition is the addition of both the size and direction of each quantity.
The resultant vector shows the result of two or more vectors acting simultaneously.

20. Practice
An airplane’s speedometer reads 500 mph North. What is the net velocity of the airplane in each case?
Wind is blowing North at 50 mph.
Wind is blowing South at 50 mph.
Wind is blowing East at 50 mph.
500𝑚𝑝ℎ(𝑁𝑜𝑟𝑡ℎ)+50𝑚𝑝ℎ(𝑁𝑜𝑟𝑡ℎ)=550𝑚𝑝ℎ(𝑁𝑜𝑟𝑡ℎ)
500𝑚𝑝ℎ 𝑁𝑜𝑟𝑡ℎ −50𝑚𝑝ℎ(𝑆𝑜𝑢𝑡ℎ)=450𝑚𝑝ℎ(𝑁𝑜𝑟𝑡ℎ) 50
500𝑚𝑝ℎ(𝑁𝑜𝑟𝑡ℎ)+50𝑚𝑝ℎ(𝐸𝑎𝑠𝑡)
500
𝑎 2 + 𝑏 2 = 𝑐 2
C=502mph

21. Examples: Pushing on a wall, Bat & Ball, Rockets
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.
Examples: Pushing on a wall, Bat & Ball, Rockets
F1 = − F2

22. Newton's Laws in Action
Friction on the tires provides necessary centripetal acceleration.
Passengers continue straight ahead in original direction and as car turns the door comes toward passenger – 1st Law
As car turns you push against door and the door equally pushes against you – 3rd Law
Section 3.4

23.
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?

24. 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!
p = mv

25. Conservation of Momentum
If we have a system of masses, the linear momentum is the sum of all individual momentum vectors.
pf = pi (final = initial)
p = p1 + p2 + p3 + … (sum of the individual momentum vectors)
Section 3.7

26. Law of Conservation of Linear Momentum
Law of Conservation of Linear Momentum - the total linear momentum of an isolated system remains the same if there is no external, unbalanced force acting on the system
Linear Momentum is ‘conserved’ as long as there are no external unbalance forces.
It does not change with time.
Section 3.7

27. Conservation of Linear Momentum
pi = pf = (for man and boat)
When the man jumps out of the boat he has momentum in one direction and, therefore, so does the boat.
Their momentums must cancel out! (= 0)
Section 3.7

28. Applying the Conservation of Linear Momentum
Two masses at rest on a frictionless surface. When the string (weightless) is burned the two masses fly apart due to the release of the compressed (internal) spring (v1 = 1.8 m/s).
Section 3.7

29. Applying the Conservation of Linear Momentum
Two masses at rest on a frictionless surface. When the string (weightless) is burned the two masses fly apart due to the release of the compressed (internal) spring (v1 = 1.8 m/s).
GIVEN:
m1 = 1.0 kg
m2 = 2.0 kg
v1 = 1.8 m/s, v2 = ?
pf = pi = 0
pf = p1 + p2 = 0
p1 = -p2
m1v1 = -m2v2
Section 3.7

30. Applying the Conservation of Linear Momentum
m1v1 = -m2v2  v2 = = = m/s
m1v1 m2
(1.0 kg) (1.8 m/s)
2.0 kg
Section 3.7

31. Jet Propulsion
Jet Propulsion can be explained in terms of both Newton’s 3rd Law & Linear Momentum
p1 = -p2  m1v1 = -m2v2
The exhaust gas molecules have small m and large v.
The rocket has large m and smaller v.
BUT  m1v1 = -m2v2 (momentum is conserved)
Section 3.7

32. 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
𝑝=𝑚𝑣= 4535𝑘𝑔 𝑂𝑚 𝑠 =0
b) 300 lb (136 kg) football player running 10 mph (4.46 m/s)
𝑝=𝑚𝑣= 136𝑘𝑔 𝑚 𝑠 =606.56𝑘𝑔∗𝑚/𝑠
c) 150 lb (68 kg) sprinter running 22 mph (9.83 m/s)
𝑝=𝑚𝑣= 68𝑘𝑔 9.83𝑚/𝑠 =668𝑘𝑔∗𝑚/𝑠
d) 1200 kg car moving at 1 m/s
𝑝=𝑚𝑣= 1200𝑘𝑔 1𝑚 𝑠 =1200kg∗m/s

33. Torque Torque – the twisting effect caused by one or more forces
As we have learned, the linear momentum of a system can be changed by the introduction of an external unbalanced force.
Similarly, angular momentum can be changed by an external unbalanced torque.
What on Earth is spin? - Brian Jones
Section 3.7

34. Torque
Torque is a twisting action that produces rotational motion or a change in rotational motion.
Section 3.7

35. Torque and Lever Arm
Torque varies with the length of the lever arm. As the length of the lever arm is doubled, the torque is doubled, for a given force.
Section 3.7

36. Law of Conservation of Angular Momentum
Law of Conservation of Angular Momentum - the angular momentum of an object remains constant if there is no external, unbalanced torque (a force about an axis) acting on it
Concerns objects that go in paths around a fixed point, for example a satellite orbiting the earth
Coffee Mug on String
Section 3.7

37. Angular Momentum L = mvr
L = angular momentum, m = mass, v = velocity, and r = distance to center of motion
L1 = L2
m1v1r1 = m2v2r2
Section 3.7

38. Angular Momentum - Example
Mass (m) is constant.
As r changes so must v. When r decreases, v must increase so that m1v1r1 = m2v2r2
Section 3.7

39. Angular Momentum in our Solar System
In our solar system the planet’s orbit paths are slightly elliptical, therefore both r and v will slightly vary during a complete orbit.
Section 3.7

40. Conservation of Angular Momentum Example
A comet at its farthest point from the Sun is 900 million miles, traveling at 6000 mi/h. What is its speed at its closest point of 30 million miles away?
EQUATION: m1v1r1 = m2v2r2
GIVEN: v2, r2, r1, and m1 = m2
FIND: v1 = =
v2r2 r1
(6.0 x 103 mi/h) (900 x 106 mi)
30 x 106 mi
1.8 x 105 mi/h or 180,000 mi/h
Section 3.7

41. Conservation of Angular Momentum
Rotors on large helicopters rotate in the opposite direction
Section 3.7

42. Conservation of Angular Momentum
Figure Skater – she/he starts the spin with arms out at one angular velocity. Simply by pulling the arms in the skater spins faster, since the average radial distance of the mass decreases.
m1v1r1 = m2v2r2
m is constant; r decreases;
Therefore v increases
Section 3.7

43. Angular momentum is momentum in a circular path.
The angular momentum vector is perpendicular to the plane of the circular path.
L = mvr L v
MIT Physics Demo -- Bicycle Wheel Gyroscope

44. How does momentum affect the force of impact?
Football player hits referee
Mythbusters - Car crash force
During an impact, the force of impact depends on how quickly the momentum is changed.
Examples:
Water barrels at the start of a divided highway
Carpet vs. concrete
F = Dp t

45. Practice
F = Dp t
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 𝑓 − 𝑝 𝑖 𝑡 = 2075𝑘𝑔 0𝑚 𝑠 −(2075𝑘𝑔)( 30𝑚 𝑠 ) .5𝑠 =124,500𝑁
𝐹= 𝑝 𝑓 − 𝑝 𝑖 𝑡 = 2075𝑘𝑔 0𝑚 𝑠 −(2075𝑘𝑔)( 30𝑚 𝑠 ) .5𝑠 =124,500𝑁

46. How is conservation of momentum applied?
The total momentum of an isolated system remains constant.
Examples: Collisions & Ice Skaters
pf = pi
Lf = Li
Bike Tires and Conservation of Angular Momentum
World Record Figure Skating Spin

47. Always assume momentum is conserved.
Practice
Always assume momentum is conserved.
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?
L = mvr
Assuming L is constant…her v must increase to 15 m/s

48. Newton’s Law of Gravitation
Gravity is a fundamental force of nature
We do not know what causes it
We can only describe it
Law of Universal Gravitation – Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
How to Think About Gravity - Jon Bergmann
Section 3.5

49. What is Newton’s description of gravity?
Newton’s Universal Law of Gravitation
Mutual force of attraction
All masses pull the same on each other!
Causes acceleration due to gravity, g = 9.81 m/s2
Fg = GMm d2
G is the universal gravitational constant
G = 6.67 x N.m2/kg2 G:
is a very small quantity
thought to be valid throughout the universe
was measured by Cavendish 70 years after Newton’s death
not equal to “g” and not a force

50. Newton’s Law of Gravitation
The forces that attract particles together are equal and opposite
F1 = -F or m1a1 = -m2a2
Section 3.5

51. Newton's Law of Gravitation
Gm1m2 r2
F =
For a homogeneous sphere the gravitational force acts as if all the mass of the sphere were at its center
Section 3.5

52. Applying Newton’s Law of Gravitation
Two objects with masses of 1.0 kg and 2.0 kg are 1.0 m apart. What is the magnitude of the gravitational force between the masses?
Section 3.5

53. Applying Newton’s Law of Gravitation – Example
Two objects with masses of 1.0 kg and 2.0 kg are 1.0 m apart. What is the magnitude of the gravitational force between the masses?
Gm1m2 r2
F =
(6.67 x N-m2/kg2)(1.0 kg)(2.0 kg)
(1.0 m)2
F = 1.3 x N
Section 3.5

54. 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?
𝐹=𝐺 𝑀𝑚 𝑟 2 = 6.67𝑥 10 −11 𝑁⋅ 𝑚 2 𝑘𝑔 2 (6𝑥 𝑘𝑔)(75𝑘𝑔) (6.4𝑥 10 6 𝑚) 2 =733𝑁

55. What are some effects of gravity?
Weightless Astronaut Pushes Herself With a Single Hair | NASA ISS Space Science HD
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.
Falling Faster Than g

56. Practice
If you were standing on a scale in the elevator that measured your weight, how would the scale reading change as the elevator
Accelerates up
Accelerates down
Free falls

57. Changing Earth-Moon System
Gravity Effects
Orbits
Tides
Atmospheres
Changing Earth-Moon System
Changing Earth-Moon system:
Earth’s rotation is slowing ( seconds/century)
Our Moon is drifting away (3.8 cm/year)
The synchronous orbit of the Moon (same face)
The fundamentals of space-time: Part 1 - Andrew Pontzen and Tom Whyntie

58. Photo Source: Standard HMCO copyright line
“Weightlessness” in space is the result of both the astronaut and the spacecraft ‘falling’ to Earth at the same rate
Photo Source: Standard HMCO copyright line
Section 3.5

59. Practice: The Sun's tidal affects are weak compared to the Moon. Why?
NASA | Tidal Forces on Earth
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.
The curvature of Space-Time
Hyperbolic Funnel Donation Box

60. More Mass = More Curvature
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
Gravitational Waves Hit The Late Show