1. The Burns WCI Physics Department
Physics SPH3U Forces
The Burns
WCI Physics Department

2. May the Force be with You
SPH3U: Lecture 1
Dynamics
How and why do objects move
In other words, the study of Forces
May the Force be with You

3. The Laws of Motion Force Mass Newton’s first law Newton’s second law
Newton’s third law
Examples
Isaac Newton’s work represents one of the greatest contributions to science ever made by an individual.
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4. Dynamics
Describes the relationship between the motion of objects in our everyday world and the forces acting on them
Language of Dynamics
Force: The measure of interaction between two objects (pull or push). It is a vector quantity – it has a magnitude and direction
Mass: The measure of how difficult it is to change object’s velocity (sluggishness or inertia of the object)
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5. Forces The measure of interaction between two objects (push or pull)
Vector quantity: has magnitude and direction
May be a contact force or a field force
Contact forces result from physical contact between two objects
Field forces act between disconnected objects
Also called “action at a distance”
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6. Forces Gravitational Force Buoyancy Force Friction Force Tension Force
Spring Force
Normal Force
Electric Force
Magnetic Force
And a whole bunch more…
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7. Newton’s First Law
An object subject to no external forces is at rest or moves with a constant velocity if viewed from an Inertial Reference Frame (IRF).
If NO forces act on an object, then there is NO acceleration of that object.
The following statement can be thought of as the definition of Inertial Reference Frames.
An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”.
Dude, if you leave an object alone, it does what ever it was doing before.

8. Is Waterloo a good IRF? Is Waterloo accelerating? YES!
Waterloo is on the Earth.
The Earth is rotating.
What is the acceleration of Waterloo?
T = 1 day = 8.64 x 104 sec,
R ~ RE = 6.4 x 106 meters .
Plug this in: aU = .034 m/s2 ( ~ 1/300 g)
Close enough to 0 that we will ignore it.
Therefore Waterloo is a pretty good IRF.
Let me do the calculations for you, since this is a topic we have not yet discussed.

9. Get ready to Hang on… those vector things are going be used.
Vector Nature of Force
Vector force: has magnitude and direction
Net Force: a resultant force acting on object
You must use the rules of vector addition to obtain the net force on an object
Get ready to Hang on… those vector things are going be used.

10. Newton’s First Law
If viewed from an Inertial Reference Frame (IRF). An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force
An object at rest remains at rest as long as no net force acts on it
An object moving with constant velocity continues to move with the same speed and in the same direction (the same velocity) as long as no net force acts on it
Dude, if you leave an object alone, it does what ever it was doing before.
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11. Newton’s First Law
If viewed from an Inertial Reference Frame (IRF). An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force
When forces are balanced, the acceleration of the object is zero (there is no push or pull on the object).
Object at rest: v = 0 and a = 0
Object in motion: v  0 and a = 0
The net force is defined as the vector sum of all the external forces exerted on the object. If the net force is zero, forces are balanced. When forces are balanced, the object can be stationary, or move with constant velocity.
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12. Mass and Inertia
Every object continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by unbalanced forces impressed upon it
Inertia is a property of objects
to resist changes is motion!
Mass is a measure of the
amount of Inertia.
Mass is a measure of the resistance of an object to changes in its velocity
Mass is an inherent property of an object
Scalar quantity and SI unit: kg
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13. For any object, FNET = F = ma.
Newton’s Second Law
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass
For any object, FNET = F = ma.
The acceleration a of an object is proportional to the net force FNET acting on it.
The constant of proportionality is called “mass”, denoted m.
This is the definition of mass and force.
The mass of an object is a constant property of that object, and is independent of external influences. The force is the external influence. The acceleration is a combination of these two things.
Newton’s first law explains what happens to an object when no forces act on it: it either remains at rest or moves in a straight line with constant speed. So, what will happen to an object if the net force is not zero? Newton’s 2nd law answers this question.
The force will change the motion of the object and create an acceleration. Newton’s 2nd law states the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Let’s take a look of this experiment: imagine pull a block of mass across a frictionless horizontal surface. When we exert F1 on the block, it moves with an acceleration of a1. If we apply a force twice as great on the same block, the acceleration doubles. If we increase force to 3F1, the acceleration triples.
Dude, this definition of Mass is know as the Inertial Mass. What is cool is that there is another type of Mass called Gravitational Mass. But, be patient my younglins, all will become clear in the future.
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14. Newton’s Second Law For any object, FNET = F = ma.
This strange symbol just means add of all the forces on the mass. Hey, did you notice that Forces are vectors?
For any object, FNET = F = ma.
The acceleration a of an object is proportional to the net force FNET acting on it.
The constant of proportionality is called “mass”, denoted m.
This is the definition of mass and force.
The mass of an object is a constant property of that object, and is independent of external influences.
The force is the external influence
The acceleration is a combination of these two things
Force has units of [M]x[L / T2] = kg m/s2 = N (Newton)

15. FNET = ma Newton’s Second Law... What is a force?
A Force is a push or a pull.
A Force has magnitude & direction (vector).
Adding forces is just adding force vectors. a a F1
FNET = ma F1
FNET F2 F2

16. More about Newton’s 2nd Law
You must be certain about which body we are applying it to
Fnet must be the vector sum of all the forces that act on that body
Only forces that act on that body are to be included in the vector sum
Net force component along an
axis gives rise to the acceleration
along that same axis

17. Sample Problem
One or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 and are directed along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle q = 30° and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the puck along the x-axis?
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18. Sample Problem
One or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 and are directed along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle q = 30° and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the puck along the x-axis?
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19. Sample Problem
One or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 and are directed along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle q = 30° and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the puck along the x-axis?
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20. Sample Problem
One or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 and are directed along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle q = 30° and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the puck along the x-axis?
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21. Law 3: Forces occur in pairs: FA ,B = - FB ,A
Newton’s Third Law
Law 3: Forces occur in pairs: FA ,B = - FB ,A
If object A and object B interact, the force exerted by object A on object B is equal in magnitude but opposite in direction to the force exerted by object B on object A
Equivalent to saying a single isolated force cannot exist

22. Newton’s Third Law cont.
For every action there is an equal and opposite reaction
F12 may be called the action force and F21 the reaction force
Actually, either force can be the action or the reaction force
The action and reaction forces act on different objects
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23. Some Action-Reaction Pairs
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24. Gravitational Force Nice to Know
Gravitational force is a vector
Expressed by Newton’s Law of Universal Gravitation:
G – gravitational constant
M – mass of the Earth
m – mass of an object
R – radius of the Earth
Direction: pointing downward
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25. Weight
The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object: w = mg
g can also be found from the Law of Universal Gravitation
Weight has a unit of N
Weight depends upon location
R = 6,400 km
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26. Forces We will consider two kinds of forces: Contact force:
This is the most familiar kind.
I push on the desk.
The ground pushes on the chair...
A spring pulls or pushes on a mass
A rocket engine provides some number of Newtons of thrust (1 lb of thrust = mg = 2.205*9.81 = Newtons)
Action at a distance:
Gravity
Electricity
Magnetism

27. Contact forces: Objects in contact exert forces.
Convention: Fa,b means “Force acting on a due to b”.
So Fhead,thumb means “the force on the head due to the thumb”.
The Force
Fhead,thumb

28. Let’s look at normal forces
Force from a solid surface which keeps object from falling through
Direction: always perpendicular to the surface
Magnitude: depends on situation
Let’s look at normal forces

29. Hey Dudes, Same Rope, therefore same Magnitude
Tension Force: T
A taut rope exerts forces on whatever holds its ends
Direction: always along the cord (rope, cable, string ……) and away from the object
Magnitude: depend on situation
The force the rope exerts is away from the object and parallel to the rope
When a rope attached to an object is pulling it, the magnitude of that force is the tension in the rope T1
T1 = T = T2 T2
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30. Surface Friction...
Friction is caused by the “microscopic” interactions between the two surfaces:

31. Friction Force What does it do?
It opposes relative motion of two objects that touch!
How do we characterize this in terms we have learned (forces)?
Friction results in a force in the direction opposite to the direction of relative motion (kinetic friction, static – impending motion) j N
FAPPLIED i ma
fFRICTION
some roughness here mg

32. Surface Friction... Force of friction acts to oppose relative motion:
Parallel to surface.
Perpendicular to Normal force. j N F i ma fF mg

33. Static Friction Matches up to the usN, never greater
Static Friction, ƒs
Static Friction Matches up to the usN, never greater
Just enough force to keep object at rest.
ms is coefficient of static friction
N is the normal force f F

34. f F Kinetic Friction, ƒk mk is coefficient of kinetic friction
Friction force opposes
direction of motion
N is the normal force F

35. Kinetic Friction
Woof!
Parallel to surface, opposing direction of motion
Kinetic friction depends only on two variables: the materials in question and the weight of the object. Changing the surface area in contact does not change the Kinetic friction.
Kinetic friction for most materials is less than the Static friction. Exceptions include metals, which have Static and Kinetic friction coefficients that are essentially the same, and very small surfaces, where molecular attraction forces take over.

36. Coefficients of Friction

37. Understanding Analysis
An empty cart is being rolled across a warehouse floor. If the cart was filled, the force of kinetic friction between the cart and the floor would
Decrease
Increase
Remain the same
The wheels are rolling, there is no sliding friction.
Read the question carefully, The Burns is trying to trick you

38. Understanding Analysis
Sand is often placed on an icy road because the sand:
Decreases the coefficient of friction between the tires of a car and the road
Increases the coefficient of friction between the tires of a car and the road
Decrease the gravitational force on a car
Increases the normal force of a car on the road

39. Free Body Diagram
The most important step in solving problems involving Newton’s Laws is to draw the free body diagram
Be sure to include only the forces acting on the object of interest
Include any field forces acting on the object
Do not assume the normal force equals the weight
F hand on book
So far, we have discussed Newton’s laws and analyzed several particular forces. We can start to work out some problems using Newton’s laws. The most important step in solving problems involving Newton’s Laws is to draw the free body diagram. The free body diagram can simplifies the problem. Free-body diagrams are 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 is reflects the magnitude of the force. The direction of the arrow shows the direction which the force is acting. Each force arrow in the diagram is labeled to indicate the exact type of force.
Be sure to include only the forces acting on the object of interest. Include any field forces acting on the object.
F Earth on book
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40. The Free Body Diagram...
Consider the following case as an example of this….
What are the forces acting on the plank ?
Other forces act on F, W and E. focus on plank
P = plank
F = floor
W = wall
E = earth
FW,P
FP,W
FP,F
FP,E
FF,P
FE,P

41. The Free Body Diagram... Consider the following case
What are the forces acting on the plank ?
Isolate the plank from
the rest of the world.
FW,P
FP,W
FP,F
FP,E
FF,P
FE,P

42. The Free Body Diagram...
The forces acting on the plank should reveal themselves...
FP,W
FP,F
FP,E

43. Aside... In this example the plank is not moving...
It is certainly not accelerating!
So FNET = ma becomes FNET = 0
This is the basic idea behind statics, which we will discuss later.
FP,W
FP,F
FP,E
FP,W + FP,F + FP,E = 0

44. Tools: Pegs & Pulleys Used to change the direction of forces
An ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude: F1
ideal peg
or pulley
| F1 | = | F2 | F2

45. Tools: Pegs & Pulleys Used to change the direction of forces
An ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude:
FW,S = mg mg T m
T = mg

46. Force and acceleration Understanding
A block weighing 4 lbs is hung from a rope attached to a scale. The scale is then attached to a wall and reads 4 lbs. What will the scale read when it is instead attached to another block weighing 4 lbs? ? m m m
(1)
(2)
(a) 0 lbs (b) 4 lbs (c) 8 lbs.

47. Hints for Problem-Solving
Read the problem carefully at least once
Draw a picture of the system, identify the object of primary interest, and indicate forces with arrows
Label each force in the picture in a way that will bring to mind what physical quantity the label stands for (e.g., T for tension)
Draw a free-body diagram of the object of interest, based on the labeled picture. If additional objects are involved, draw separate free-body diagram for them
Choose a convenient coordinate system for each object
Apply Newton’s second law. The x- and y-components of Newton second law should be taken from the vector equation and written individually. This often results in two equations and two unknowns
Solve for the desired unknown quantity, and substitute the numbers
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48. Balanced and Unbalanced Forces
When the forces on an object produce a net force of 0N, the forces are balanced.
There is no change in the motion of the object.

49. Balanced and Unbalanced Forces
When the net force on an object is not 0 N, the forces on the object are unbalanced.
Unbalanced forces produce a change in motion of an object.

50. Objects in Equilibrium (Balanced Forces)
Objects that are either at rest or moving with constant velocity are said to be in equilibrium
Acceleration of an object can be modeled as zero:
Mathematically, the net force acting on the object is zero
Equivalent to the set of component equations given by

51. Equilibrium, Example 1
A lamp is suspended from a chain of negligible mass
The forces acting on the lamp are
the downward force of gravity
the upward tension in the chain
Applying equilibrium gives
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52. Equilibrium, Example 2
Hang-On Guys. The Burns is going a very hard problem (man this dude is crazy).
A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37° and 53° with the horizontal. Find the tension in each of the three cables.
Conceptualize the traffic light
Assume cables don’t break
Nothing is moving
Categorize as an equilibrium problem
No movement, so acceleration is zero
Model as an object in equilibrium
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53. Equilibrium, Example 2 Need 2 free-body diagrams
Apply equilibrium equation to light
Apply equilibrium equations to knot
Analyze, cont.
Find T3 from applying equilibrium in the y-direction to the light
Find T1 and T2 from applying equilibrium in the x- and y-directions to the knot
Finalize
Think about different situations and see if the results are reasonable
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54. Accelerating Objects
If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it
Draw a free-body diagram
Apply Newton’s Second Law in component form
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55. Accelerating Objects, Example 1
A man weighs himself with a scale in an elevator. While the elevator is at rest, he measures a weight of 800 N.
What weight does the scale read if the elevator accelerates upward at 2.0 m/s2?
What weight does the scale read if the elevator accelerates downward at 2.0 m/s2? mg N mg N
Upward:
Downward: