1. Forces in one dimension
Chapter 4

2. Chapter Objectives Section 4.1 Define force. Learn how to draw FBD’s
Use Newton’s 2nd law to solve problems.
Explain the meaning of Newton’s 1st law.
Section 4.2
Describe how the weight and mass of an object are related.
Differentiate between actual weight and apparent weight.
Section 4.3
Define Newton’s 3rd law.
Explain the tension in ropes and strings in terms of Newton’s 3rd law.
Define the normal force.
Determine the value of the normal force by applying Newton’s 2nd law.

3. Force and Motion
Chapter 4 Section 1

4. Force A force is a push or pull exerted on an object.
Forces can cause an object to speed up, slow down or change direction.
A forces causes a change in an object’s velocity.
A force causes an object to accelerate.
Symbol: F
Vector Quantity
Units: newtons (N)
1 N = 1 kgm/s2
1N ≈ ¼ lb
Forces are categorized in two ways:
contact force vs. field force
the four fundamental forces of nature

5. 2 Main Types of Forces Contact Forces Field Forces
When an object from the external world touches a system and thereby exerts a force on it.
Examples:
Frictional force
Tension force
Applied force
Forces that are exerted on an object without contact.
Examples:
Gravitational force
Magnetic force
Electric force

6. 4 Fundamental Forces of Nature
Although you can think of hundreds of different forces, physicists group them all into just four categories.
Strong Nuclear Force
Force of very short range that holds the particles in the nucleus together
The strongest of the four forces
Weak Force
Involved in the radioactive decay of some nuclei.
Actually a form of the EM force
Gravitational Force
An attractive force that exists between all objects
The weakest of the four forces
Electromagnetic Force
A force due to electric charges, both static and moving.
Second strongest of the forces

7. Agents and Systems
Since forces are caused by interactions (whether there is contact or not), you should be able to determine the cause of the force and what the force is acting on.
The Agent
The thing the causes the force
The System The thing that the force is acting on.
You should be able to label the agent and the system.

8. Example – Labeling the Agent and System
If I push a book with my hand across a table…
System
Agent
…the book is the system and my hand is an agent.

9. Don’t forget the force of gravity!
Models of Forces
You can use a pictorial model to help you analyze how force affects motion.
Steps for Making a Pictorial Model:
Sketch the situation.
Circle the system.
Identify every place where the system touches the external world. (This is where contact forces are exerted.)
Identify the contact forces and label.
Then identify any field forces on the system.
Force of table on book
Force of hand on book
Don’t forget the force of gravity!

10. Free-Body Diagrams (FBD)
A physical model that represents the forces acting on a system.
The system is represented using a particle model.
Represent all forces acting on the system with an arrow that points away from the particle.
Label all forces.
F hand on book
F table on book
Don’t forget the force of gravity!
F table on book
F hand on book Fg

11. Assignment
We are going to do some practice problems together on whiteboards.
For each problem do the following:
Draw pictorial model and FBD
Specify the system in the pictorial model.
Label all forces with their agents in both.
Draw vectors of appropriate lengths in FBD.

12. Some Types of Forces
Please become familiar with these forces – you will see them often!
Force
Symbol
Definition
Direction
Friction Ff
The contact forces that acts to oppose sliding motion between surfaces
Parallel to the surface and opposite the direction of sliding
Normal FN
The contact force exerted by a surface on an object
Perpendicular to and away from the surface
Spring
Fsp
The push or pull a spring exerts on an object
Opposite the displacement of the object at the end of the spring

13. Some Types of Forces Force Symbol Definition Direction Tension FT
The pull exerted by a string, rope, or cable when attached to a body and pulled taut
Away from the object and parallel to the string, rope, or cable at the point of attachment
Weight Fg
A field force due to the gravitational attraction between two objects, usually Earth and an object
Straight down toward the center of Earth - ALWAYS
Applied FA
A generic term for a push or pull exerted by a person on an object.
In the direction of the push or pull.
Please become familiar with these forces – you will see them often!

14. Newton’s Laws of Motion
Newton’s 1st Law: An object with no net force acting on it remains at rest or moves with a constant velocity in a straight line.

15. Newton’s Laws of Motion
Newton’s 2nd Law: The acceleration of an object is directly proportional to the net force on it and inversely proportional to its mass.
a = Fnet / m or Fnet = ma

16. Newton’s Laws of Motion
Newton’s 3rd Law: When one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude but opposite in direction.

17. Newton’s First Law Balanced Forces
The motion of an object will continue as it was (at the same speed and in a straight line) unless acted upon by an unbalanced force.
Balanced Forces
Balanced forces acting on an object produce a net force = 0
The forces “cancel” each other out.
Unbalanced Forces
Unbalanced forces acting on an object produce a net force ≠ 0
The forces do not “cancel” each other out.

18. 4-2 Newton’s First Law The tendency of an object to resist change.
Inertia
Equilibrium
The tendency of an object to resist change.
If an object is at rest, it tends to remain at rest.
If an object is in motion, it tends to continue moving as it was.
Inertia is not a force.
When the net force on an object is equal to zero, the object is said to be in equilibrium.
An object is at equilibrium when it is:
at rest OR
moving at a constant velocity

19. Combining Forces Net Force (Fnet)
The vector sum of all of the forces acting on a system.
Net force is equal to the resultant
can be determined graphically or mathematically.
Graphically: Mathematically:
100 N
200 N
300 N
So the Fnet = 300 N to the right
75 N
25 N
(-75 N) +
(25 N)
-50 N
So the Fnet = 50 N to the left

20. You Try – Example 1
Two horizontal forces, 225 N and 165 N, are both exerted on a canoe to the right. Find the net horizontal force on the canoe.

21. You Try – Example 2
Two horizontal forces are exerted in opposite directions on a canoe. If 225 N is exerted to the left and 165 N to the right, find the net horizontal force on the canoe.

22. You Try – Example 3
Three confused sled dogs are trying to pull a sled across the Alaskan snow. Snowball pulls east with a force of 35 N, Rudolf also pulls east but with a force of 42 N, and big Diesel pulls west with a force of 53 N. What is the net force on the sled?

23. Using Newton’s Second Law
Steps for Determining How Forces Effect the Motion of an Object :
Identify all forces acting on the object (Pictorial Model is useful here)
Draw a free body diagram
Add forces to find the net force
Use Newton’s 2nd to find acceleration.
*Use constant acceleration equations from chapter 3 (if necessary) to find displacement or velocity.

24. Physics Theory - Bell Ringer
Consider a cart moving along a straight line, moving at a constant speed…
Because the velocity is not changing, does this mean there are no forces acting on the cart?
No, the Earth and the track both exert forces on the cart. There are also forces due to air resistance and friction.
If identifiable agents are exerting forces on the cart, then why is there no change in velocity? The net force on the cart is zero.

25. Practice Problems Practice Determining Net Force: p. 93, # 6-8
Practice Using Newton’s 2nd Law:
p. 113, #61
p. 114, #

26. Using Newton’s Laws
Chapter 4 Section 2

27. Using Newton’s Laws
What is the force of gravity?
How can you calculate weight?
The gravitational force exerted by a large body, usually Earth, is called weight.
Weight is measured in newtons like all other forces.
You can you figure out the weight of an object with mass, m, if you know the acceleration due to gravity, g.
The weight of an object can be found using Newton's 2nd Law.

28. Weight
This force is called the weight of an object and given the special symbol “W”. So,
W = mg
*Remember, weight and mass are not the same thing.
Mass is the amount of matter something contains.
Weight is the gravitational pull on an object. It depends on mass and gravity.
The weight of an object can be found using Newton's 2nd Law. F = ma a = g The force of gravity is given by the equation: F = mg

29. Apparent Weight
What is Apparent Weight?
Does Your Apparent Weight Change?
Whatever force is pushing upward on us we interpret as our "weight"- not our true weight - that is the force due to gravity ”mg".
This upward force is what we interpret as our APPARENT WEIGHT. 
If you accelerate in a vertical direction, your weight will appear different
Accelerating up, apparent weight increases
Accelerating down, apparent weight decreases
Why? Picture an Elevator…
N = mg if the elevator is at rest or moving at constant velocity
N = mg + ma if the elevator has an upward acceleration
N = mg - ma if the elevator has a downward acceleration

30. Weightlessness Weightlessness
Definition
Weightlessness
Weightlessness
When an object has an apparent weight of zero due to the lack of contact forces pushing up on the object.
Remember - It is the UPWARD FORCE that we feel on us - not gravity!
All people/things who are ONLY subjected to gravity are freely falling and feel weightless.

31. Drag Force
Drag Force
Drag Force Example
The force exerted by a fluid on an object moving through the fluid
Depends on:
object's properties
object’s motion
fluid’s properties

32. Terminal Velocity
Terminal Velocity
Terminal Velocity Pictorial Model
The constant velocity of an object that is reached when the drag force equals the force of gravity.
Drag
Force Fg
Drag
Force Fg Fg
Body released from rest
Forces on body during acceleration
Forces on body at terminal velocity

33. Homework
4.2 Section Review Questions
p. 101 #

34. Interaction Forces
Chapter 4 Section 3

35. Interaction Forces One force does not cause the other force.
Remember Newton’s 3rd Law
Forces act in pairs
FA on B = - FB on A
Interaction Pair
Two forces that are opposite in direction and have equal magnitude and act on different objects.
Also called action-reaction pairs
One force does not cause the other force.
They act together or not at all.
Fball on table
Ftable on ball

36. Action-Reaction Pairs
A block of mass m rests on a table. You apply a small force to the block, but the block does not move. Which of the following are action-reaction pairs according to Newton’s 3rd Law?
The force due to gravity acting on the block and the normal force acting on the block
The block’s gravitational pull on Earth and Earth’s gravitational pull on the block
The applied force on the block and the frictional force on the block
The block’s push on the table and the table’s push on the block

37. Normal Force What is the Normal Force?
It is the contact force exerted by a surface on another object.
The normal force is ALWAYS perpendicular to the surface.
Draw in the normal force for each situation at the right.

38. Forces of Ropes and Strings
Tension Force
Example
Tension is a specific name for the force exerted by a rope, string, or cable.
The tension in the rope is equal to the weight of the object hanging from it when the object is in equilibrium.
The tension will not be the same as the weight if the object is accelerating.
Draw a free body diagram for this situation. (The bucket is at rest.)
FT (rope on bucket)
Fg (Earth’s mass on bucket)

39. Tension Problems – Example
A 50.0 kg bucket is being lifted by a rope. The rope will not break if the tension is 525 N or less. The bucket started at rest, and after being lifted 3.0 m, it is moving at 3.0 m/s. If the acceleration is constant, is the rope in danger of breaking?

40. Tension Problems – Example Solution
Calculations:
Fnet = FT - Fg
FT = Fnet + Fg
Fnet = ma
Fg = mg
FT = ma + mg
FT = m(a + g)
vf2 = vi2 + 2ad
vf2 = 0 + 2ad
a = vf2 / 2d
FT = m[(vf2 / 2d) + g]
Calculations:
FT = m[(vf2 / 2d) + g]
FT = 50.0g [(3.0m/s)2 / (2)3.0m + (9.8m/s2)]
FT = 50.0g [(9.0m2/s2 / 6.0m) + 9.8m/s2]
FT = 50.0g [(1.5 m/s2) + 9.8m/s2]
FT = 50.0g (11.3 m/s2)
FT = 565 N
Max Tension of Rope = 525 N or more
So, yes, the rope is in danger of breaking because the tension exceeds 525 N.
FT (rope on bucket)
Fg (Earth’s mass on bucket)
Given: m = 50.0 kg vi = 0.0 m/s vf = 3.0 m/s d = 3.0 m g = 9.8 m/s2 FT = ?
Equations:
Fnet = FT - Fg
Fnet = ma
Fg = W = mg
vf2 = vi2 + 2ad

41. Tension Problem – You Try!
You are fishing and catch a fish with a mass of 6 kg. If the fishing line can withstand a maximum tension of N, what is the maximum acceleration you can give the fish as you reel it in?
Answer:
amax = 5 m/s2

42. Homework – Interaction Forces
Section Review Q’s: pg. 107 #34-39 Practice Problem: pg. 106 #32

43. Bell Ringer See the diagram on the board.
Two boys on roller skates are each holding the end of a rope. If one boy pulls on the rope, what will happen?
Will they accelerate?
In which direction will they accelerate, if any?
Who’s acceleration will be greater? Or will they be equal?

44. Chapter 4 Review Problems
FYI - Ch 4 Test is Wednesday, Nov 5th!
Please complete the following problems to help you review for the test.
p #53, 59-61, 64, 70, 73, 80, 84, 88(a&b)
Note - This is an IN CLASS assignment – it will be checked at the end of class today so that we may discuss all of the answers tomorrow.
You may work in groups – help each other work through the problems, don’t just copy your classmates work.