1. EQ: How do forces affect motion?
Unit 3: Forces
EQ: How do forces affect motion?

2. The Meaning of Force
Force: a push or pull upon an object resulting from the object’s interaction with another object.
Force is a vector quantity.
For simplicity sake, all forces (interactions) between objects can be placed into two categories:
Contact Forces
Action-at-a Distance Forces

3. Contact Forces: those types of forces that result when two interacting objects are perceived to be physically contacting each other.
Action-at-a-Distance Forces: those types of forces that result even when the two interacting objects are not in physical contact with each other, yet are able to exert a push or pull despite their physical separation.
Newton: the amount of force required to give a 1-kg mass an acceleration of 1 m/s2. The standard unit of measurement for force.
1 Newton (N) = 1 kg ∙ m/s2

4. Action-at-a-Distance Forces
Types of Forces
Contact Forces
Action-at-a-Distance Forces
Frictional Force
Gravitational Force
Tension Force
Electrical Force
Normal Force
Magnetic Force
Air Resistance Force
Applied Force
Spring Force

5. Fapp Fnorm Ffrict Fair Ftens Fspring Type of Force Description Symbol
Applied Force
A force that is applied to an object by a person or another object.
Fapp
Gravitational Force
The force with which the earth, moon, or other massively large object attracts another object towards itself. Gravity is directed downward toward the center of the earth. The weight of an object.
Fgrav
= mg
m= mass in kg
g= 9.8 N/kg
Normal Force
The support force exerted upon an object that is in contact with another stable object. (Ex. Book on a desk)
Fnorm
Friction Force
The force exerted by a surface as an object moves across it or makes an effort to move across it. (Sliding, static)
Ffrict
Air Resistance Force
A special type of force that acts upon objects as they travel through the air. It opposes the motion of the object.
Fair
Tension Force
The force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. (Tug-of-War)
Ftens
Spring Force
The force exerted by a compressed or stretched spring upon any object that is attached to it.
Fspring

6. Types of Friction
Sliding Friction: results when an object slides across a surface. (Ex: pushing a box across a floor)
Static Friction: results when the surfaces of two objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object. (Ex: pushing a couch across a carpeted floor - what you must overcome in order to get the couch to move)

7. Fluid Friction: results when a solid object moves through a fluid
Fluid Friction: results when a solid object moves through a fluid. (Ex: bird flying through the air, fish moving through water)
Rolling Friction: results when an object rolls across a surface. (Ex: bicycle wheel rolling over the road)

8. Mass vs. Weight
The force of gravity acting upon an object is sometimes referred to as the weight of the object. It is related to the pull of gravity on the object and is altered by location.
The mass of an object refers to the amount of matter that is contained by the object. Mass is never altered by location, the pull of gravity, speed, or even the existence of other forces.

9. Check Your Understanding
Different masses are hung on a spring scale calibrated in Newtons. (Fgrav = mg)
The force exerted by gravity on 1 kg = 9.8N.
The force exerted by gravity on 5 kg = _____N.
The force exerted by gravity on _____kg = 98N.
The force exerted by gravity on 70 kg = _____N.
2) When a person diets, is their goal to lose mass or to lose weight? Explain.

10. Drawing Free-Body Diagrams
Free-Body Diagrams: diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.
The size of the arrow in a free-body diagram reflects the magnitude of the force while the tip of the arrow shows the direction that the force is acting.

11. Fnorm
Ffrict
Fapp
Fgrav

12. Guided Practice
A book is at rest on a tabletop. Diagram the forces acting on the book.
A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on the combination of girl and bar.
An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.
A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel.

13. Graded Practice
A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.
A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.
A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack.

14. A skydiver is descending with a constant velocity
A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver.
A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Neglect air resistance. Diagram the forces acting on the sled.
A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. Diagram the forces acting upon the football as it rises upward towards its peak.
A car is coasting to the right and slowing down. Neglect air resistance. Diagram the forces acting upon the car.

15. Determining Net Force
Net Force: the vector sum of all the forces that act upon an object. =
= 0 = = = 5 5 10 5 -5 5 10 15 5
-10 -5 5
-15
-10 -5 5 10

16. Guided Practice 1200 N 50 N 600 N 20 N 800 N 50 N 800 N Fnet = 400N up
Fnet = 200N down
Fnet = 20N left

17. Does a Net Force Exist?

18. Graded Practice 1 3N 3N A B 5N 5N 5N 3N 3N
40N
20N C D
20N
25N

19. Graded Practice 2 300N B Fnet = 0 N Fnet = 60N, left A 50N 80N D 200N
Fnet = 900N, up
Fnet = 30N, right
200N H

20. Forces Practice Worksheet 1 Design an Experiment Activity Formative Assessment 1

21. Sir Isaac Newton Biography https://www.youtube.com/watch?v=YPRV1h3CGQk

22. Newton’s First Law of Motion
Isaac Newton, a 17th century scientist, put forth a variety of laws that explain why objects move (or don’t move) as they do.
These laws are known as Newton’s Three Laws of Motion.
Newton’s First Law of Motion: an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Sometimes referred to as the law of inertia.

23. (same speed and direction)
Forces are Balanced
Stay in Motion
(same speed and direction)
Objects in Motion
(v ≠ 0 m/s)
Objects at Rest
(v = 0 m/s)
Stay at Rest
a = 0 m/s2
a = 0 m/s2

24. Balanced vs. Unbalanced Forces
Balanced Forces: Equal in magnitude, opposite in direction. Also known as equilibrium.
Unbalanced Forces: Forces not in equilibrium.

25. Inertia: the resistance to a change in motion.
Everyday Examples of Newton’s First Law:
A car stopping suddenly. The force of the road on the locked wheels provides the unbalanced force to change the car’s state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. What stops you from continuing through the windshield?
Your seat belt!
The seat belt provides the unbalanced force that brings you from a state of motion to a state of rest.

26. Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator.
A brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer. (Don’t try this at home!)
To dislodge ketchup from the bottom of the ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.
Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard.

27. Inertia and Mass
Before Newton, it was believed that it was the natural tendency of an object to come to rest. Eventually moving objects would stop moving; a force was necessary to keep an object in motion.
Galileo, a premier scientist in the 17th century, developed the concept of inertia. He reasoned that moving objects eventually stop because of a force called friction. In experiments using a pair of inclined planes facing each other, Galileo observed that a ball would roll down one plane and up the opposite plane to approximately the same height. If smoother planes were used, the ball would roll up the opposite plane even closer to the original height.

28. Galileo reasoned that any difference between initial and final heights was due to the presence of friction. He postulated that if friction could be entirely eliminated, then the ball would reach exactly the same height each time.
He further observed that regardless of the angle in which the planes were oriented, the final height was almost always equal to the initial height.
If the opposite incline were elevated at nearly a 0-degree angle, then the ball would roll almost forever in an effort to reach the original height.

29. Isaac Newton built on Galileo’s thoughts about motion
Isaac Newton built on Galileo’s thoughts about motion. His first law declares that a force is not needed to keep an object in motion, rather one is needed to get it to stop.
In the absence of friction, an object would continue in motion with the same speed and direction – forever!
All objects resist change in motion – but some have more of a tendency to resist change more than others.
The tendency of an object to resist changes in its state of motion varies with mass.

30. The more mass an object has, the more inertia it has.

31. Check Your Understanding
Imagine a place in the cosmos far from all gravitational and frictional influences. Suppose that you could visit that place and throw a rock. The rock will
a) gradually stop
b) continue in motion in the same
direction at constant speed

32. A 2-kg object is moving horizontally with a speed of 4 m/s
A 2-kg object is moving horizontally with a speed of 4 m/s. How much net force is required to keep the object moving at this speed and in this direction?
Mac and Tosh are arguing in the cafeteria. Mac says that if he flings the Jell-O with a greater speed it will have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. Who do you agree with?
Supposing you were in space in a weightless environment, would it require a force to set an object in motion?

33. Fred spends most Sunday afternoons at rest on the sofa, watching pro football games and consuming large quantities of food. What affect (if any) does this practice have upon his inertia? Explain.
Ben Tooclose is being chased through the woods by a bull moose that he was attempting to photograph. The enormous mass of the bull moose is intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton’s first law of motion.

34. Two bricks are resting on the edge of the lab table
Two bricks are resting on the edge of the lab table. Shirley Sheshort stands on her toes and spots the two bricks. She acquires an intense desire to know which of the two bricks is most massive. Since Shirley is vertically challenged, she is unable to reach high enough to lift the bricks, she can however reach high enough to give the bricks a push. Discuss how the process of pushing the bricks will allow Shirley to determine which of the two bricks is most massive. What difference will Shirley observe and how can this observation lead to the necessary conclusion?

35. Answers B
0-N An object in motion will remain in motion unless acted upon by an unbalanced force.
Tosh. Inertia depends solely on mass.
Yes! Even in space, an object has mass which means it has inertia. A force must be used to set an object in motion.
If Fred continues this habit, his mass will increase thus causing his inertia to increase.
The moose has a large mass which means it has a large inertia. This large inertia requires more force to change the moose’s state of motion.
The brick with the greater mass will have more resistance to motion and will require a larger force to set into motion.

36. Newton’s Second Law of Motion
According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it.
The presence of an unbalanced force will accelerate an object – changing its speed, its direction, or both.
Newton’s second law of motion pertains to the behavior of objects for which all existing forces are not balanced.

37. The above equation is often rearranged to a more familiar form:
Newton’s Second Law of Motion: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
a = Fnet m
The above equation is often rearranged to a more familiar form:
Fnet = ma

38. As the force acting upon an object is increased, the acceleration of the object is increased.
As the mass of an object is increased, the acceleration of the object is decreased.
The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration is in the same direction as the net force; an acceleration is produced by a net force.
So, what am I trying to get across?

39. It is not just any ole force that is used in the equation, it is the NET FORCE!
Reminder: The net force is the vector sum of all the forces acting upon an object.
Practice
Net Force (N)
Mass (kg)
Acceleration (m/s2) 10 2 20 4 5

40. The numerical information in the preceding table demonstrates some important qualitative relationships between force, mass, and acceleration.
Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant).
Comparing the values in rows 2 and3, it can be seen that a doubling of the mass results in a halving of the acceleration (if the force is held constant).
The direction of the net force is in the same direction as the acceleration.

41. Check Your Understanding
Determine the accelerations that result when a 12N net force is applied to a 3 kg object then to a 6 kg object.
A net force of 15N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s2. Determine the mass of the encyclopedia.
Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?
Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?

42. Answers
4 m/s2; 2 m/s2
3.0 kg
3 m/s2
12 m/s2

43. Motion Misconceptions
Sustaining motion requires a force.
Two students are discussing their physics homework prior to class. They are discussing an object that is being acted upon by two individual forces (both in a vertical direction); the free-body diagram for the particular object is shown below.
Fnorm = 20N
Fgrav = 20N

44. During the discussion, Anna Litical suggests to Noah Formula that the object under discussion could be moving. In fact, Anna suggests that if friction and air resistance could be ignored, the object could be moving in a horizontal direction.
Noah objects, arguing that the object could not have any horizontal motion if there are only vertical forces acting upon it. Noah claims that the object must be at rest, perhaps on a table or floor. After all, says Noah, an object experiencing a balance of forces will be at rest. Who do you agree with?

45. Answer
Anna is correct.
Noah Formula may know his formulas but he does not know (or does not believe) Newton's laws. If the forces acting on an object are balanced and the object is in motion, then it will continue in motion with the same velocity. Remember: forces do not cause motion. Forces cause accelerations.

46. Finding Acceleration Guided Practice
a = Fnet m 1) An applied force of 50N is used to accelerate an object to the right across a frictional surface. The object encounters 10N of friction. Use the diagram to determine the normal force, the mass, and the acceleration of the object. (Neglect air resistance)
Fnorm = _______
Ffrict = 10N
Fapp = 50N
Fgrav = 80N

47. An applied force of 20N is used to accelerate an object to the right across a frictional surface. The object encounters 10N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance)
Fnorm = ________
Ffrict = 10N
Fapp = 20N
Fgrav = 100N

48. Guided Practice
Imagine you throw a baseball that weighs 0.1kg with a force of 100N. What is the acceleration of the baseball?
An arrow leaves the bow with a force of 500N. The mass of the arrow is 250kg. What is its acceleration?
A dog has a mass of 20kg. If the dog is pushed across the ice with a force of 40N, what is its acceleration?

49. Graded Practice
Suppose a student pushes a cart of groceries with a 40kg mass. How much force does he use if the cart accelerates 2.5 m/s2?
A bag of charcoal has a mass of 10kg. Two bags were added to the cart of groceries mentioned in problem 1. If the student pushes with a force of 90N, what is the acceleration of the cart?
If the acceleration of the cart with the added mass of the two bags of charcoal is increased to 2.5 m/s2, how much additional force must be applied to the cart?

50. Answers
100N
1.5 m/s2
60N

51. Terminal Velocity
The free-body diagrams below show the forces acting upon an 85-kg skydiver.
As the skydiver falls, he picks up speed. The increase in speed leads to an increase in the amount of air resistance. Eventually the air resistance becomes large enough to balance the force of gravity. At this instance, the net force becomes 0N and the skydiver will quit accelerating. He has reached terminal velocity.
700N
350N
833N
833N
833N
833N

52. Forces Practice Worksheet 2

53. Answers 6000N 30N 5000N 2.5 m/s2 10 m/s2 2500 kg 20 m/s2 4N 50 m/s2

54. Formative Assessment 2 Weight and Second Law Math Practice Net Force Practice

55. Newton’s Third Law of Motion
Newton’s Third Law of Motion: For every action, there is an equal and opposite reaction.
Forces always come in pairs – action-reaction.
The size of the forces are equal.
The direction of the forces are opposite.

56. Examples of Interaction Force Pairs
Fish Swimming: A fish uses its fins to push water backwards as the water pushes the fish forward.
Birds Flying: The wings of the bird push downward and the air is pushing the bird upwards.
Car Moving: As the wheels of the car spin, they grip the road and push the road backward as the road pushes the car forward.

57. Check Your Understanding
For years, space travel was believed to be impossible because there was nothing that rockets could push off of in space in order to provide the propulsion necessary to accelerate. This inability of a rocket to provide propulsion is because…
…space is void of air so the rockets have nothing to push off of.
…gravity is absent in space.
…space is void of air and so there is no air resistance in space
…nonsense! Rockets do accelerate in space and have been able to do so for a long time.

58. Many people are familiar with the fact that a rifle recoils when fired
Many people are familiar with the fact that a rifle recoils when fired. This recoil is the result of action-reaction force pairs. A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. Consistent with Newton’s Third Law of Motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is…
…greater than the acceleration of the bullet.
…smaller than the acceleration of the bullet.
…the same size as the acceleration of the bullet.

59. In the top picture, Kent Budgett is pulling upon a rope that is attached to a wall. In the bottom picture, Kent is pulling upon a rope that is attached to an elephant. In each case, the force scale reads 500N. Kent is pulling…
…with more force when the rope is attached to the wall.
…with more force when the rope is attached to the elephant.
…the same force in each case.

60. Answers
Answer: D
It is a common misconception that rockets are unable to accelerate in space. The fact is that rockets do accelerate. There is indeed nothing for rockets to push off of in space - at least nothing which is external to the rocket. But that's no problem for rockets. Rockets are able to accelerate due to the fact that they burn fuel and push the exhaust gases in a direction opposite of the direction which they wish to accelerate.

61. Answer: B
The force on the rifle equals the force on the bullet. Yet, acceleration depends on both force and mass. The bullet has a greater acceleration due to the fact that it has a smaller mass. Remember: acceleration and mass are inversely proportional.
Answer: C
Kent is pulling with 500 N of force in each case. The rope transmits the force from Kent to the wall (or to the elephant) and vice versa. Since the force of Kent pulling on the wall and the wall pulling on Kent are action-reaction force pairs, they must have equal magnitudes. Inanimate objects such as walls can push and pull.

62. Identifying Action-Reaction Forces
Identify at least six pairs of action-reaction pairs in the following diagram.

63. Answers
The elephant's feet push backward on the ground; the ground pushes forward on its feet.
The right end of the right rope pulls leftward on the elephant's body; its body pulls rightward on the right end of the right rope.
The left end of the right rope pulls rightward on the man; the man pulls leftward on the left end of the right rope.
The right end of the left rope pulls leftward on the man; the man pulls rightward on the right end of the left rope.
The tractor pulls leftward on the left end of the left rope; the left end of the left rope pulls rightward on the tractor.
The tractor’s wheels push backward on the ground; the ground pushes forward on the wheels.

64. What Makes a Bug Go Splat?
Splat! A bug has just flown into the windshield of an oncoming car. The car must have hit the bug much harder than the bug hit the car, right?

65. Buzz: In order for the bug to fly through the air, a force has to push the bug forward. Identify this force. How does the bug produce it? (Hint. Think back to how a swimmer moves through the water)
Air pushes the bug forward. The bug produces this force by pushing backward on the air with its wings, and the reaction force is that the air pushes forward on the bug.

66. The bug was at rest on a tree when it saw the car and decided to fly toward it. If the bug has a mass of 0.05 kg and accelerates at 2 m/s2, what’s the net force on the bug?
0.05 kg x 2 m/s2 = 0.1 N

67. Vroom: The driver hates killing bugs
Vroom: The driver hates killing bugs. When she saw one coming toward the windshield, she braked suddenly and hoped it would get out of the way. (Sadly, it did not.) When she hit the brakes, she felt that she was thrown forward. Use one of Newton’s laws to explain why.
Newton’s first law says that objects in motion stay in motion. The car stopped but she kept moving forward.

68. Splat: The unfortunate bug hits the windshield with a force of 1 N
Splat: The unfortunate bug hits the windshield with a force of 1 N. If you call this the action force, what is the reaction force? Does the car hit the bug any harder than the bug hits the car? Use one of Newton’s laws to explain why or why not.
The windshield hits the bug with a 1 N force. No; Newton’s third law states that for every force, there is an equal and opposite force.

69. Compare the forces on the bug and the car again
Compare the forces on the bug and the car again. Use another one of Newton’s laws to explain why the bug goes splat and the car keeps going, without noticeably slowing down.
Newton’s second law; The same force acts on both, but the bug has a much smaller mass, so it accelerates much more.
Newton’s first law; The bug is not massive enough to stop the car or change it’s motion.

70. Assess Your Understanding
A dog pulls on his leash with a 10 N force to the left, but doesn’t move. Identify the reaction force.
The leash pulls on the dog with a 10 N force to the right.

71. Using all three of Newton’s laws, explain how objects react to forces.
Sample: Newton’s first law states objects change their motion when force is applied. Newton’s second law says the acceleration depends on the strength of the force and the mass of the object. Newton’s third law says that whenever a force acts on an object, that object applies an equal and opposite force back.

72. Momentum
The sports announcer says, “Going into the all-star break, the St. Louis Cardinals have the momentum.” The headlines declare “St. Louis Blues Gaining Momentum.” The coach pumps up his team at half-time saying, “You have the momentum; the critical need it that you use that momentum and bury them in the third quarter.”
Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop.

73. Momentum = mass ∙ velocity
Momentum, however, is a physics term referring to the quantity of motion that an object has. If an object is in motion, then it has momentum.
Momentum: mass in motion (vector quantity)
Momentum is dependent upon two things: how much stuff is moving (mass) and how fast the stuff is moving (velocity).
Momentum = mass ∙ velocity
p = mv
Units: kg ∙ m/s
An object at rest does not have momentum.

74. 180kg x 16 m/s = 2880 kg∙m/s to the right
Guided Practice
A lioness has a mass of 180 kg and a velocity of 16 m/s to the right. What is her momentum?
180kg x 16 m/s = 2880 kg∙m/s to the right
The warthog has a mass of 100 kg. What does the warthog’s speed have to be for it to have the same momentum as the lioness?
28.8 m/s

75. Graded Practice Find the momentum of the following:
A 60 kg halfback is moving eastward at 9 m/s.
A 1000 kg car is moving northward at 20 m/s.
A 40 kg freshman is moving southward at 2 m/s.
A car possesses 20,000 units of momentum. What be the car’s new momentum if…
…its velocity was doubled?
…its velocity was tripled?
…its mass was doubled (by adding more passengers and a greater load)?
…both it’s velocity and mass were doubled?

76. A halfback (m= 60 kg), a tight end (m= 90 kg), and a lineman (m= 120 kg) are running down the football field. Consider their ticker tape patterns below.
Compare the velocities of these three players. How many times greater are the velocity of the halfback and the velocity of the tight end than the velocity of the lineman? Which player has the greatest momentum and why?

77. Answers 1) a) 540 kg∙m/s b) 20,000 kg∙m/s c) 80 kg∙m/s
d) 80,000 kg∙m/s
Tight End: covers twice the distance in the same amount of
time (v = 6 m/s)
Halfback: covers three times the distance in the same
amount of time (v = 9 m/s)
The tightend and the halfback both have a momentum of
540 kg∙m/s, while the lineman only has a momentum of
360 kg∙m/s

78. Law of Conservation of Momentum
In the absence of an outside force (friction), the total momentum of objects that interact does not change.
The total momentum of any group of objects remains the same, or is conserved, unless outside forces act on the objects.

79. Non-sticky Collisions
When two objects of the same mass (100 kg) collide and don’t stick together and outside forces are negligible, the objects trade velocities. The car that is going faster before the collision will end up slowing down, and the car that is going slower before the collision will end up speeding up. Therefore, the momentums are the same.

80. Car 1: Car 2: m = 100 kg m = 100 kg v = 4 m/s v = 2 m/s M = 400 kg∙m/s M = 200 kg∙m/s Total M = 600 kg∙m/s After Collision: v = 2 m/s v = 4 m/s M = 200 kg∙m/s M = 400 kg∙m/s

81. Sticky Collisions
Sometimes objects end up sticking together during a collision. Two cars, which have the same mass, got tangled together after they collided. Since one car was at rest and had a momentum of zero, only the other car had any momentum before the collision. After they collided and stuck together, the cars shared that momentum. The total momentum of the two cars stayed the same.

82. Check Your Understanding
How can a heavy moving van have the same momentum as a small motorcycle?
Momentum equals mass times velocity, so the truck would need to be moving more slowly than the motorcycle.
What is the momentum of a 750 kg car traveling at a velocity of 25 m/s?
750 kg x 25 m/s = kg∙m/s

83. The total momentum of two marbles before a collision is 0. 06 kg∙m/s
The total momentum of two marbles before a collision is 0.06 kg∙m/s. No outside forces act on the marbles. What is the total momentum of the marbles after the collision?
0.06 kg∙m/s

84. Inertia v. Momentum How are inertia and momentum related?
Inertia is the measure of how much resistance matter has to acceleration. The more inertia something has, the less it wants to respond to forces and accelerate. This statement is mathematically stated a = F/m. (Newton’s Second Law) The more force, the more acceleration. The more inertia, the less acceleration.
Momentum is the product of inertia (m) and velocity (v). p=ma. The more inertia something has, the more momentum it has, when in motion.

85. Predictions for the Year 3000