1. Forces & the Laws of Motion
Chapter 4

2. Mechanics
Kinematics
Dynamics

3. Mechanics: Kinematics and Dynamics
Mechanics: Study of motion and its causes
Kinematics: Descriptions of motion
Displacement
Velocity
Acceleration
Dynamics: Causes of Motion
Force
Net Force, Fnet
Force Equilibrium

4. 4.1 Changes in Motion Objectives:
Explain how force affects the motion of an object
Distinguish between contact forces and field forces
Interpret and construct free-body diagrams

5. Force
What is a force?
A push or pull that can change the motion of an object
So a force can cause what? _______________
What is the SI unit for force?
The newton (N)
One newton is the force required to accelerate a 1-kg mass at 1 m/s2
1N = 1 kg·m/s2 1N = lbf 1lbf = N

6. Forces act through contact or at a distance
Contact forces:
Forces that affect an object through physical contact with another object
Example: a baseball bat hitting a baseball
Field forces:
Forces that affect an object without physical contact
Examples: gravitational, magnetic, and electrostatic forces

7. Field Theory
Explains how forces can affect an object without physical contact
Explanation of field forces…
An object affects the space surrounding it so that a force is exerted on other objects in that space.
The “field” is the region of space in which the force is exerted
The “field” exerts the force on the object
Example: magnetic field

8. Electrostatic Force
An example of a field force

9. Force Diagrams Force is a vector quantity Force diagrams:
Diagram the objects involved in a situation and the forces acting on all the objects
Free-body diagrams:
Diagram the forces acting on a single object
i.e. diagram the forces acting on a single object

10. Representing Forces Forces are vector quantities
Free-body diagrams illustrate forces acting on an object isolated from its surroundings

11. Free-body Diagrams
Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon a single object in a given situation
Represent object as a point with forces originating from center
The object is simplified as a point mass rather than an extended object (one with 3 dimensions)

12. Example of a Free-Body Diagram

13. Common Forces in Force Diagrams
Applied force Fapp
Weight Fg or W (mg)
Normal force FN or N ┴ to surface
Friction Ff
Air resistance Fair
Tension Ft or T ropes, cables
Spring force Fsp

14. Force Equilibrium Force equilibrium All forces “cancel”
No net force acting on an object
Can an object in force equilibrium be in motion?

15. Force equilibrium
A book of mass 0.50 kg is at rest on a table. Calculate the normal force, FN.
Since the book is at rest, force equilibrium exists
Construct a free-body drawing then solve

16. 4.2 Newton’s First Law: Law of Inertia
Galileo noted that things tend to slide further on smoother surfaces
Concluded that an object would slide forever on a perfectly smooth surface in the absence of any applied force
This led to Newton’s First Law of Motion

17. Newton’s First Law of Motion: Inertia
An object at rest remains at rest, and an object in motion continues in motion at a constant velocity unless acted upon by a net external force

18. 4.2 Galileo’s Experiments

19. Newton’s First Law of Motion

20. Inertia
Inertia is tendency of an object to maintain its state of motion
Mass is a measurement of inertia (inertial mass)
↑ mass → ↑ inertia
As the same speed, a rolling car is more difficult to stop than a rolling basketball
i.e. because the car has more mass, more force is required

21. Newton’s First Law of Motion
An object at rest remains at rest, and an object in motion continues in motion with a constant velocity unless acted upon by a net external force
A net force is required to change the state of motion of an object
Net external force
Resultant force produced from combination of all forces acting on an object

22. Object on an inclined plane
How could an object slide down the ramp if gravity acts vertically downward?

23. Forces Acting on an object on an Inclined Plane
FN, normal force, surface acting on object
Fg, weight = mg
Fgx, component of g, ║ to surface
Fgy, component of g ┴ surface
Ff, friction

24. Calculating Net External Force
Identify variables & select equation
Draw free-body diagram and apply coordinate system
Calculate x & y components of all vectors
Calculate x & y components of the resultant Fnet (Fx, Fy)
Calculate net external force (Fnet)

25. Equilibrium The state of a body in which there is no change in motion
Net force acting on a body is zero

26. 4.3 Newtons 2nd & 3rd Laws Learning objectives
Describe acceleration of an object in terms of its mass and the net external force acting on it
Predict direction & magnitude of acceleration caused by a known net external force
Identify action-reaction force pairs
Explain why action-reaction pairs do not result in equilibrium

27. Newtons 2nd Law
The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object
a = ΣF /m , where Σ means “sum of”
ΣF = ma

28. Conceptual Question
A grain truck filled with soy beans accelerates along the highway at 0.50 m/s2. If the driving force on the truck remains the same, what happens to the acceleration of the truck if soybeans leak from it at a constant rate?
Answer: The loss of soy beans is a decrease in mass. Since a = ΣFnet /m , acceleration increases.

29. Newton’s 3rd Law of Motion
When one body exerts a force on a second body, the first body experiences a force that is equal in magnitude but opposite in direction to the force it exerted.
FAB = - FBA
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.

30. Newton’s 3rd Law
"For every action, there is an equal and opposite reaction." equal magnitude and opposite direction
In every interaction, there is a pair of forces acting on the two interacting objects.
Action-reaction force pairs: equal in magnitude, but opposite in direction.

31. Action-Reaction Force Pairs
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.
Since force pairs are equal in magnitude, but opposite in direction, why do they not result in equilibrium?
Because they act on different objects.
If equal but opposite forces acted on the same object, there would be equilibrium, i.e. no net force.

32. Comparison of Newton’s Laws
First Law
Inertia
No formula
Second Law
Acceleration
ΣF = ma
Third Law
Interaction
FAB = -FBA

33. 4.4 Everyday Forces Weight Normal Force
Force of gravity acting on a mass
Fg = mg W = mg Fw = mg
Normal Force
contact force exerted by one object on another in a direction ┴ surface of contact
Friction
contact force that opposes motion….
opposes applied force

34. Weight, Gravity & the Normal Force
Gravitational force causes objects to accelerate toward earth
F=ma or Fg = mg
An object’s weight is the force of gravity acting on the object, so…
W = mg
If gravity acts on falling objects, does it act on objects at rest?
If Fnet = ma, why do the objects remain at rest?

35. The Normal Force
According to Newton’s 2nd law, for an object to be at rest, there must be no net force acting on the object
If gravity is acting on the object, then there must be another force opposing gravity, such that ΣF = 0
This opposing force is called the normal (perpendicular) force, Fn
Fn is the force of the surface supporting the object

36. Normal Force
A force exerted by one object on another in a direction perpendicular to the surface of contact
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.

37. Normal Force

38. Suppose a box of mass 20.0 kg sits at rest on a level table.
Determine the weight of the box and the normal force exerted by the table on the box
since the box is at rest, Σ Fy = Fn - mg = 0
Fn = mg = 20.0kg x 9.81m/s2 = N
b) Suppose a brick weighing 16.0 N is set on top of the box. Determine the normal force.
Σ Fy = Fn N - mg = 0
Fn = mg N = N N = N

39. Suppose a box of mass 20.0 kg sits at rest on a level table.
Suppose the brick is removed and a rope is tied around the box. A vertical force of 16.0 N is applied to the box by pulling on the rope. What is the normal force?
Σ Fy = FN N - mg = 0
FN = mg – 16.0N = N – 16.0 N = N

40. Suppose a box of mass 20.0 kg sits at rest on a level table.
c) Suppose the rope is directed at an angle of 30 deg with a tension of 16.0 N. What is the normal force?
ΣFy=0
FN = mg
ΣFy=0
FN + FAy = mg
FN = mg – Fay
FN = N – 8.0 N
FN = N mg mg

41. Forces of Friction
National Institutes of Health, via Wikimedia Commons

42. Force of Friction
Friction is a force that opposes relative motion between systems in contact

43. Force of Friction Ff opposes applied force
Acts parallel to the surfaces in contact
Depends on surfaces in contact….
Types and smoothness
Proportional to Fn

44. Types of Friction Static friction Fs …. Kinetic friction Fk ….
force exerted by environment on motionless body to resist applied force
Kinetic friction Fk ….
force exerted by environment on moving object to resist applied force
Fs > Fk

45. Role of Surface in Friction
Frictional forces are due to interaction of surfaces
Mechanical
Electrostatic attractions at the molecular level
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.

46. The Role of Normal Force in Friction
With increasing Fn, more surface comes in contact
This increases the amount of mechanical obstruction and molecular adhesion between the surfaces
© , Rice University. Except where otherwise noted, content created on this site is licensed under a Creative Commons Attribution 4.0 License.

47. Quantifying the Relationship of Ff and Fn
Ff is proportional to Fn
Proportionality constant is the coefficient of friction, μ
μ = Ff / Fn
Depends on types of surfaces in contact
Depends on static or kinetic friction
μs = Fs / Fn μk = Fk / Fn

48. Problem 4D
A crate of mass 24 kg is set in motion on a horizontal surface with a horizontal force of 75 N. Find the coefficient of static friction, μs
μs = Fs / FN
= Fs / mg
= 75 N / (24 kg x 9.81 m/s2)
= 0.32

49. Frictional & Applied Force
Static friction increases with increasing force until overcome
Kinetic friction is less than the maximum static friction

50. Coefficients of Friction (Approximate)
Materials μs μk
Steel on steel
0.74
0.57
Waxed wood on wet snow
0.14
0.10
Aluminum on steel
0.61
0.47
Waxed wood on dry snow
----
0.04
Rubber on dry concrete
1.00
0.80
Metal on metal (lubricated)
0.15
0.06
Rubber on wet concrete
0.50
Ice on ice
0.03
Wood on wood
0.40
0.20
Teflon on Teflon
Glass on glass
0.90
Synovial joints in humans
0.01
0.003

51. Air Resistance When an object passes through a fluid….
The fluid has to be pushed out of the way for the object to pass through it
i.e., Motion of objects through a fluid is hindered by the fluid

52. Air Resistance At low speeds FR is proportional to v
At higher speeds FR is proportional to v2
When FR = FA, constant speed
Terminal speed
For free falling object
When FR up = Fg down
Fnet = 0

53. Four Fundamental Forces
All are field forces
Strong nuclear force
Holds nucleus together
Weak nuclear force
Involved in radioactive decay
Electromagnetic force
Gravitational force
weakest