1. Chapter 4
The Laws of Motion

3. 4.1 Classes of Forces
Contact forces 接觸力 involve physical contact between two objects
Field forces 場力 act through empty space
No physical contact is required
Fig 4.1

4. More About Forces
A spring can be used to calibrate the magnitude of a force

5. Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object

6. Fig 4.3

7. 4.2 Newton’s First Law
If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration
This is also called the law of inertia慣性定律
It defines a special set of reference frames called inertial frames慣性座標系,
We call this an inertial frame of reference

8. Isaac Newton ( )

9. Inertial Frames
Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame
A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame
We can consider the Earth to be such an inertial frame although it has a small centripetal acceleration associated with its motion

10. Newton’s First Law – Alternative Statement
In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity
Newton’s First Law describes what happens in the absence of a force
Also tells us that when no force acts on an object, the acceleration of the object is zero

11. 4.3 Inertia and Mass
The tendency of an object to resist any attempt to change its velocity is called inertia
Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity

12. More About Mass Mass is an inherent property of an object
independent of the object’s surroundings
independent of the method used to measure it
a scalar quantity
The SI unit of mass is kg

13. Mass vs. Weight 質量 vs 重量 Mass and weight are two different quantities
Weight is equal to the magnitude of the gravitational force exerted on the object
Weight will vary with location
The mass of an object is the same everywhere

14. 4.4 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
Force is the cause of change in motion, as measured by the acceleration
Algebraically,

15. More About Newton’s Second Law
is the net force
This is the vector sum of all the forces acting on the object
Newton’s Second Law can be expressed in terms of components:

16. Units of Force

18. Fig 4.4

21. 4.5 Gravitational Force
The gravitational force, , is the force that the earth exerts on an object
This force is directed toward the center of the earth
Its magnitude is called the weight of the object
Weight = Fg = mg

22. More About Weight
Because it is dependent on g, the weight varies with location
g, and therefore the weight, is less at higher altitudes
Weight is not an inherent property of the object

23. Gravitational Mass vs. Inertial Mass
In Newton’s Laws, the mass is the inertial mass and measures the resistance to a change in the object’s motion
In the gravitational force, the mass is determining the gravitational attraction between the object and the Earth
Experiments show that gravitational mass and inertial mass have the same value

25. 4.6 Newton’s Third Law
If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1
Note on notation: is the force exerted by A on B

26. Newton’s Third Law, Alternative Statements
Forces always occur in pairs
A single isolated force cannot exist
The action force is equal in magnitude to the reaction force and opposite in direction
One of the forces is the action force, the other is the reaction force
It doesn’t matter which is considered the action and which the reaction
The action and reaction forces must act on different objects and be of the same type

27. Action-Reaction Examples, 1
The force
exerted by object 1 on object 2 is equal in magnitude and opposite in direction to exerted by object 2 on object 1
Fig 4.5

28. Fig 4.5

29. Action-Reaction Examples, 2
The normal force (table on monitor) is the reaction of the force the monitor exerts on the table
Normal means perpendicular, in this case
The action (Earth on monitor) force is equal in magnitude and opposite in direction to the reaction force (the monitor exerts on the Earth)
Fig 4.6(a)

30. Free Body Diagram
In a free body diagram, you want the forces acting on a particular object
The normal force and the force of gravity are the forces that act on the monitor
Fig 4.6(b)

31. CONCEPTUAL EXAMPLE Third law clarification
CONCEPTUAL EXAMPLE Third law clarification. Michelangelo’s assistant has been assigned the task of moving a block of marble using a sled. He says to his boss, “When I exert a forward force on the sled, the sled exerts an equal and opposite force backward. So how can I ever start it moving? No matter how hard I pull, the backward reaction force always equals my forward force, so the net force must be zero. I’ll never be able to move this load.” Is this a case of a little knowledge being dangerous? Explain.

32. Fig 4.7

33. 4.7 Applications of Newton’s Law
Assumptions
Objects can be modeled as particles
Masses of strings or ropes are negligible
When a rope attached to an object is pulling it, the magnitude of that force, , is the tension in the rope, along the rope away from the object

34. Objects in Equilibrium
If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium
Mathematically, the net force acting on the object is zero

35. Fig 4.9

36. Problem-Solving Hints Newton’s Laws
Conceptualize the problem – draw a diagram
Categorize the problem
Equilibrium (SF = 0) or Newton’s Second Law (SF = m a)
Analyze
Draw free-body diagrams for each object
Include only forces acting on the object

37. Problem-Solving Hints Newton’s Laws, cont
Analyze, cont.
Establish coordinate system
Be sure units are consistent
Apply the appropriate equation(s) in component form
Solve for the unknown(s)
Finalize
Check your results for consistency with your free- body diagram
Check extreme values

38. Newton’s Second Law, Example 1a
Forces acting on the crate:
A tension, the magnitude of force
The gravitational force,
The normal force, , exerted by the floor
Fig 4.8

39. Newton’s Second Law, Example 1b
Apply Newton’s Second Law in component form:
Solve for the unknown(s)
If is constant, then a is constant and the kinematic equations can be used to more fully describe the motion of the crate

40. A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in Figure 4.10a. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain in this situation, or will one of the cables break?

41. Analyze Need two free-body diagrams
Apply equilibrium equation to the light and find
Apply equilibrium equations to the knot and find and
Fig 4.10(b)(c)

45. Objects Experiencing a Net Force
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

46. A child on a sled is released on a frictionless hill of angle , as in Figure 4.11a.

47. Forces acting on the object:
Determine the acceleration of the sled after it is released. A
Forces acting on the object:
The normal force acts perpendicular to the plane
The gravitational force acts straight down
Choose the coordinate system x along the incline and y perpendicular to the incline
Replace the force of gravity with its components

48. From (2) we conclude that the
n = mg cos  .

49. Suppose the sled is released from rest at the top of the hill and the distance from the front of the sled to the bottom of the hill is d. How long does it take the front of the sled to reach the bottom, and what is its speed just as it arrives at that point? B

50. Multiple Objects
When two or more objects are connected or in contact, Newton’s laws may be applied to the system as a whole and/or to each individual object
Whichever you use to solve the problem, the other approach can be used as a check

51. When two objects with unequal masses are hung vertically over a light, frictionless pulley as in Active Figure 4.12a, the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to measure the free-fall acceleration. Calculate the magnitude of the acceleration of the two objects and the tension in the string.

52. Active Figure
4.12
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53. Forces acting on the objects:
Tension (same for both objects, one string)
Gravitational force
Each object has the same acceleration since they are connected
Draw the free-body diagrams
Apply Newton’s Laws
Solve for the unknown(s)
Fig 4.12

56. To finalize the problem, let us consider some special cases
To finalize the problem, let us consider some special cases. (a) m1 = m2, (b) m2 >> m1

57. Two blocks of masses m1 and m2, with m1 > m2, are placed in contact with each other on a frictionless, horizontal surface, as in Active Figure 4.13a. A constant horizontal force is applied to m1 as shown.

58. Active Figure
4.13
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59. Find the magnitude of the acceleration of the system of two blocks.
First treat the system as a whole:

60. Apply Newton’s Laws to the individual blocks Solve for unknown(s)
Determine the magnitude of the contact force between
the two blocks. B
Apply Newton’s Laws to the individual blocks
Solve for unknown(s)
Check: |P21| = |P12|

61. Imagine that the force in Active Figure 4
Imagine that the force in Active Figure 4.13 is applied toward the left on the right-hand block of mass m2. Is the magnitude of the force the same as it was when the force was applied toward the right on m1? C

62. A person weighs a fish on a spring scale attached to the ceiling of an elevator, as shown in Figure Show that if the elevator accelerates, the spring scale reads an apparent weight different from the fish’s true weight.

63. Solution An observer on the accelerating elevator is not in an inertial frame. We need to analyze this situation in an inertial frame, so let us imagine observing it from the stationary ground.
Newton’s second law applied to the fish in the vertical direction gives us

64. For example, if the weight of the fish is 40
For example, if the weight of the fish is 40.0 N and is upward with ay = 2.00 m/s2, the scale reading is

66. 4.8 Forces on Automobiles
The force that accelerates an automobile is the friction force from the ground
The engine applies a force to the wheels
The bottom of the tires apply forces backward on the road surface and the reaction (road on tires) causes the car to move forward

67. Automobile Performance