1. Lecture 4 Dynamics: Newtons Laws of Motion
Objects undergo motion and accelerations. This is caused by an interaction between bodies. Such interactions are called forces. Recall most of our forces are contact forces
Newton’s laws of motion: Published Newton’s Principia (1642)
SHOW DEMO ILLUSTRATING INERTIA AND FORCE

2. Examples of Contact Forces:
A push or pull can be a force
Normal force
Tension in a string
Friction
Two balls colliding
Example of Noncontact forces
Gravitational force
Electric force

3. NEWTON’S FIRST LAW
An object continues in a state of rest or of motion at constant speed in a straight line unless acted upon by a net force.
If you push it and let it go, it will move at constant velocity.
Show some demos
Demo: Air levitated hockey puck sliding across table top
Demo: Heavy kilogram mass on table top
Example : Hockey puck of mass m on ice
Block of Ice

4. Newton’s First Law of Motion
Conceptual Example : Newton’s first law.
A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What force causes them to do that?
Answer: No force; the backpacks continue moving until stopped by friction or collision.

5. NEWTON’S FIRST LAW
An object continues in a state of rest or of motion at constant speed in a straight line unless acted upon by a net force.
If you don’t push it, it won’t move. A body has inertia.
Show some demos
Demo: Air levitated hockey puck sliding across table top
Demo: Heavy kilogram mass on table top
Example : Hockey puck of mass m on ice
Block of Ice

6. Inertia Another way of understanding the First Law
Inertia is a bodies resistance to change due to forces. Inertia is related to mass.
Some examples of inertia
Hit a nail in a piece of wood on an anvil sitting
on your head
Mass on string (Demo)

7. Two different ways of breaking the string: Inertia and Tension
Upper string breaks when
you pull slowly because
tension is greater
Lower string breaks when you pull quickly because of inertia
First pull fast see where it breaks
Then pull slowly see where it breaks
Explain

8. NEWTON’S SECOND LAW Sum of all external forces acting on
the body = net force on body of mass m
Newton’s second law is much more general than the first. It tells us what happens when forces acting on a body are present. A net force acting on a body from the environment produces an acceleration of the body.
The inertia of the body, as measured by its mass, resists the change in velocity caused by the force. The greater the mass, the smaller the acceleration.
It is simplest to think about Newton’s laws in the absence of friction. We can take friction into account, however, by including it as one of the forces acting on the body of interest.
SHOW Propeller driven glider timed for one unit of distance and four units. Since it takes twice as long to go four times as far, the acceleration must be constant. So the propeller is providing a nearly constant force, leading to a constant acceleration.
System Mass Acceleration Force
SI kg m/s Newton (N)
CGS g cm/s dyne (dyn)
BE slug (sl) ft/s2 pound (lb)

9. Because force is a vector we have 3 equations
relating force and acceleration each corresponding
To a different coordinate

10. Newton’s Second Law of Motion
Example 4-2: Force to accelerate a fast car. Estimate the net force needed to accelerate (a) a 1000-kg car at ½ g
Figure 4-6.
4-2. Use Newton’s second law: acceleration is about 5 m/s2, so F is about 5000 N for the car and 1 N for the apple.
4-3. First, find the acceleration (assumed constant) from the initial and final speeds and the stopping distance; a = -7.1 m/s2. Then use Newton’s second law: F = -1.1 x 104 N.

11. Example Force to stop a car.
What average net force is required to bring a 1500-kg car to rest from a speed of 30 m/s within a distance of 50 m?

12. NEWTON’S THIRD LAW
When two bodies interact, the forces on the bodies due to each other are always equal in magnitude and opposite in direction. M
Table

13. Newton’s Third Law of Motion
A key to the correct application of the third law is that the forces are exerted on different objects. Make sure you don’t use them as if they were acting on the same object.
Figure 4-9. Caption: An example of Newton’s third law: when an ice skater pushes against the wall, the wall pushes back and this force causes her to accelerate away.

14. Newton’s Third Law of Motion
Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.
Figure Caption: We can walk forward because, when one foot pushes backward against the ground, the ground pushes forward on that foot (Newton’s third law). The two forces shown act on different objects.

15. Rules for drawing free body diagrams
Rules for drawing free body diagrams. The purpose is to Isolate the forces acting on one body
Draw a diagram
Represent the body by a point.
Each force acting on the body is represented by a vector with tail at the point and the length of vector indicating the approximate magnitude of the force.
It may be convenient to resolve the forces into components
Apply Newton’s second law and solve for the unknowns

16. Weight and the force of gravity
Falling objects accelerate at the rate of 9.81 m/s2
or g.
From Newtons 2nd law, we know F= ma where a =g.
If a table or floor is in the way gravity is still acting
and trying to accelerate the object. This produces the
gravitational force acting on the object called weight.
But the object is not accelerating. Isn’t this a violation
of Newtons 2nd law
NO. Because the table or floor exerts an upward force
back on the object so that the net force is 0. This
upward force is called the Normal force.

17. What is the free body diagram of a block at rest on the table?
When you stand still on a sidewalk, you are not accelerating along the sidewalk, so there is no force on you in that direction. In that case the only force the sidewalk exerts on you is upward, opposing gravity. This force is perpendicular to the sidewalk surface. This is called a normal force. Normal is a term that refers to something being perpendicular to a surface or line. W N

18. Book leaning against a crate on a table at rest
Book leaning against a crate on a table at rest. What are the action –reaction pairs because of Newtons 3rd Law?
Table T

19. Draw a free body diagram of the forces acting
on the crate NT mg B
2) Does the crate C accelerate?

20. A crate of mass 310 kg is being pulled by a man as shown in the figure
A crate of mass 310 kg is being pulled by a man as shown in the figure. What is the acceleration of the crate along the x direction? Man does not move. N T f +y N +x W
First draw a free body diagram of the forces acting on the crate

21. Draw a free body diagram of the forces acting on the crate
y is vertical
x is horizontal N T f W
Now we want to apply Newton’s second Law to the x and y
components independently.

22. A crate of mass 310 kg is being pulled by a man as shown in the figure
A crate of mass 310 kg is being pulled by a man as shown in the figure. What is the acceleration of the crate along the x direction? Man does not move. +y N W T f N +x
x component of forces in
free body diagram

23. What is the normal force assuming there is no
acceleration in the y direction? N W T f N
y component of forces in
free body diagram

24. Problem: What is the acceleration of the system of the two blocks and the contact force between the blocks? What is the net force on Block B?
31 kg
65 N
24 kg A B B A
65 N 24

25. Problem: What is the acceleration of the system of the two blocks and the contact force between the blocks? What is the net force on Block B?
31 kg
65 N
24 kg A B
65 N A B
Student Version 25

26. Now lets look at tension in a string
Tension in the string is equal to the weight = 10 N
The scale reads the tension in the string

27. Is the tension in the string any different when I have weights pulling it down on both sides?

28. Problem 12 kg 24 kg 31 kg T3=65 N kg 31 kg 12 kg 24 kg 65 N
What is the acceleration of the system?
Find T1
Find T2 a) b) c)

29. Rev George Atwood’s machine 1746 -1807 Tutor Trinity College, Cambridge2
DEMO Atwoods Machine

30. Set up Coordinate system Assume acceleration in some direction
Draw free body diagram for each body
Apply Newtons second law to each body mg Mg T a
1) Assume mass 1 or M is going down 1 2 +y +x
DEMO Atwoods Machine

31. Free body diagram for each body and apply Newtons second law1. 2.
Free body diagram for each body and
apply Newtons second law mg Mg T a 1 2 +y +x
DEMO Atwoods Machine
Solve eq 1 and 2 for T and a

32. Free body diagram for each body and apply Newtons second law1. 2.
Free body diagram for each body and
apply Newtons second law mg Mg T a 1 2 +y +x
DEMO Atwoods Machine

33. 4-7 Solving Problems with Newton’s Laws: Free-Body Diagrams
Example 4-13: Elevator and counterweight (Atwood’s machine).
A system of two objects suspended over a pulley by a flexible cable is sometimes referred to as an Atwood’s machine. Here, let the mass of the counterweight be 1000 kg. Assume the mass of the empty elevator is 850 kg, and its mass when carrying four passengers is 1150 kg. For the latter case calculate (a) the acceleration of the elevator and (b) the tension in the cable.
Figure Caption: Example 4–13. (a) Atwood’s machine in the form of an elevator–counterweight system. (b) and (c) Free-body diagrams for the two objects.
Answer: Each mass has two forces on it, gravity pulling downward and the tension in the cable pulling upward. The tension in the cable is the same for both, and both masses have the same acceleration. Writing Newton’s second law for each mass gives us two equations; there are two unknowns, the acceleration and the tension. Solving the equations for the unknowns gives a = 0.68 m/s2 and FT = 10,500 N.

34. Another example. Find tension T in the cord and the downward acceleration a. Draw Free Body Diagram of each body M and m assuming m is accelerating down:
Frictionless pulley T
Demos for inclined planes, pulleys
Normal force and tension
Example problems Atwoods machine, Einstein in an elevator or accelerating scale, blocks accelerating T

35. Set up Coordinate system Assume acceleration in some direction Draw free body diagram for each body Apply Newtons second law to each body
Frictionless pulley +y +x
Demos for inclined planes, pulleys
Normal force and tension
Example problems Atwoods machine, Einstein in an elevator or accelerating scale, blocks accelerating T a a

36. +y +x Demos for inclined planes, pulleys Normal force and tension
Example problems Atwoods machine, Einstein in an elevator or accelerating scale, blocks accelerating

37. Demos for inclined planes, pulleys
Normal force and tension
Example problems Atwoods machine, Einstein in an elevator or accelerating scale, blocks accelerating

38. Tug-of-war demo illustrates how a small sideways force can produce a large horizontal force
Suppose two guys in the tug of war are at 4.5 meters
apart and I pull the rope out 0.15 meters. Then φ =4 degrees
2.25 m f
Therefore,
The smaller the angle the larger
the magnification
If then