1. Forces and Newton’s Laws of Motion
Chapter 4
Forces and Newton’s Laws of Motion

2. 4.1 The Concepts of Force and Mass
A force is a push or a pull.
Arrows are used to represent forces. The length of the arrow
is proportional to the magnitude of the force.
15 N
5 N

3. 4.3 Newton’s Second Law of Motion
SI Unit for Force
This unit of force is called a newton (N).

4. 4.1 The Concepts of Force and Mass
Mass is a measure of the amount
of “stuff” contained in an object.
SI Unit of Mass: kilogram (kg)

5. 4.2 Newton’s First Law of Motion
Newton’s First Law (Law of Inertia)
An object continues in a state of rest
or in a state of motion at a constant
Speed unless changed by a net force
The net force is the SUM of all
of the forces acting on an object.

6. 4.2 Newton’s First Law of Motion
The net force on an object is the sum of all forces acting on that object.
Individual Forces
Net Force
4 N
10 N
6 N

7. 4.2 Newton’s First Law of Motion
Individual Forces
Net Force
5 N
3 N
4 N

8. 4.3 Newton’s Second Law of Motion
Mathematically, the net force is
written as
where the Greek letter sigma denotes the vector sum.

9. 4.3 Newton’s Second Law of Motion
When a net force acts on an object
of mass m, the acceleration that results is
directly proportional to the net force and has
a magnitude that is inversely proportional to
the mass. The direction of the acceleration is
the same as the direction of the net force.

10. 4.4 The Vector Nature of Newton’s Second Law
The direction of force and acceleration vectors
can be taken into account by using x and y
components.
is equivalent to

11. 4.4 The Vector Nature of Newton’s Second Law

12. 4.4 The Vector Nature of Newton’s Second Law
The net force on the raft can be calculated
in the following way:
Force
x component
y component
+17 N
+(15 N) cos67
0 N
+(15 N) sin67
+23 N
+14 N

13. 4.4 The Vector Nature of Newton’s Second Law

14. 4.5 Newton’s Third Law of Motion
Whenever one body exerts a force on a
second body, the second body exerts an
oppositely directed force of equal magnitude on the first body.

15. 4.5 Newton’s Third Law of Motion
Suppose that the magnitude of the force is 36 N. If the mass
of the spacecraft is 11,000 kg and the mass of the astronaut
is 92 kg, what are the accelerations?

16. 4.5 Newton’s Third Law of Motion

17. 4.7 The Gravitational Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on every
other particle.

18. 4.7 The Gravitational Force
For two particles that have masses m1 and m2 and are
separated by a distance r, the force has a magnitude
given by

19. 4.7 The Gravitational Force

20. 4.7 The Gravitational Force

21. 4.7 The Gravitational Force
Definition of Weight
The weight of an object on or above the earth is the gravitational force that the earth exerts on the object. The weight always acts downwards, toward the center
of the earth.
SI Unit of Weight: newton (N)

22. Definition of the Normal Force
The normal force is the force that a surface
exerts on an object with which it is in contact
– It is ALWAYS perpendicular to the surface.

23. 4.8 The Normal Force
A hand pushes down on a block with a force of 11 N. The block weighs 15N. What is the magnitude of the normal force?
A rope is now used to lift the block with a force of 11 N. What is the magnitude of the normal force?

24. 4.8 The Normal Force
Apparent Weight
The apparent weight of an object is the reading of the scale.
It is equal to the normal force the man exerts on the scale.

25. 4.8 The Normal Force
true
weight
apparent
weight

26. 4.9 Static and Kinetic Frictional Forces
When an object is in contact with a surface there is a force
acting on that object. The component of this force that is
parallel to the surface is called the
frictional force.

27. 4.9 Static and Kinetic Frictional Forces
When the two surfaces are
not sliding across one another
the friction is called
static friction.

28. 4.9 Static and Kinetic Frictional Forces
Note that the magnitude of the frictional force does
not depend on the contact area of the surfaces.
What does it depend on???

29. 4.9 Static and Kinetic Frictional Forces
Static friction opposes the impending relative motion between
two objects.
Kinetic friction opposes the relative sliding motion motions that
actually does occur.
is called the coefficient of kinetic friction.

30. 4.9 Static and Kinetic Frictional Forces
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31. 4.9 Static and Kinetic Frictional Forces
The sled comes to a halt because the kinetic frictional force
opposes its motion and causes the sled to slow down.

32. 4.9 Static and Kinetic Frictional Forces
Suppose the coefficient of kinetic friction is 0.05 and the total
mass is 40kg. What is the kinetic frictional force?

33. 4.3 Newton’s Second Law of Motion
A free-body-diagram is a diagram that
represents the object and the forces that
act on it.

34. The net force in this case is: 275 N + 395 N – 560 N = +110 N
4.3 Free Body Diagrams
The net force in this case is:
275 N N – 560 N = +110 N
and is directed along the + x axis of the coordinate system.

35. 4.6 Types of Forces: An Overview
Examples of different forces:
Friction force
Tension force
Normal force
Weight (Force due to gravity)
Gravitational Force
Magnetic Force
Electric Force

36. Cables and ropes transmit forces through tension.
4.10 The Tension Force
Cables and ropes transmit
forces through tension.

37. This diagram shows four forces acting upon an object
This diagram shows four forces acting upon an object. There aren’t always four forces, For example, there could be one or more forces.

38. Problem 1
A book is at rest on a table top. Diagram the forces acting on the book.

39. Problem 1
In this diagram, there are normal and gravitational forces on the book.

40. Problem 2
An egg is free-falling from a nest in a tree. Neglect air resistance. Draw a free-body diagram showing the forces involved.

41. Gravity is the only force acting on the egg as it falls.

42. Problem 3
A rightward force is applied to a book in order to move it across a desk. Consider frictional forces. Neglect air resistance. Construct a free-body diagram. Let’s see what this one looks like.

43. Note the applied force arrow pointing to the right
Note the applied force arrow pointing to the right. Notice how friction force points in the opposite direction. Finally, there is still gravity and normal forces involved.

44. Problem 4
A block is at rest on an incline and stays in place because of static friction. Draw a free-body diagram

45. A skier is standing motionless on a horizontal tow rope, which is about to pull her forward. The skier’s mass is 59kg and the coefficient of static friction between the skis and the snow is Draw a free body diagram. What is the magnitude of the maximum force that the tow rope can apply to the skier without causing her to move.

46. Objects in Equilibrium
Objects that are either at rest or moving with constant velocity are said to be in equilibrium
This means that the net force acting on the object is zero
Equivalent to the set of component equations given by

47. 4.11 Equilibrium Application of Newton’s Laws of Motion
Reasoning Strategy
Draw a free-body diagram.
Choose a set of x, y axes for each object and resolve all forces
in the free-body diagram into components that point along these
axes.

48. 4.11 Equilibrium Application of Newton’s Laws of Motion
What is the Tension in Rope 1 and 2?
The engine has a weight of 3150 N

49. 4.11 Equilibrium Application of Newton’s Laws of Motion
Force
x component
y component

50. 4.11 Equilibrium Application of Newton’s Laws of Motion
The first equation gives
Substitution into the second gives

51. 4.11 Equilibrium Application of Newton’s Laws of Motion

52. 4.12 Nonequilibrium Application of Newton’s Laws of Motion
When an object is accelerating, it is not in equilibrium.

53. 4.12 Nonequilibrium Application of Newton’s Laws of Motion
The mass of the supertanker is 1.5 x 108 kg. There is a drive force with magnitude
75000 N and an opposing force of N. The tanker moves with an acceleration
of 2.0 x 10-3 m/s2. Solve for the Tension in each of the ropes.
The acceleration is along the x axis so

54. 4.12 Nonequilibrium Application of Newton’s Laws of Motion
Force
x component
y component

55. 4.12 Nonequilibrium Application of Newton’s Laws of Motion

56. 4.12 Nonequilibrium Application of Newton’s Laws of Motion