The Laws of Motion

1
Chapter 4

• The Laws of Motion

Conceptual questions 1,3,4,5,9,18 Quick quizzes
1,2,4,8 Problems 6,55,34,40,80
2
Classical Mechanics

• Describes the relationship between the motion of
  objects in our everyday world and the forces
  acting on them
• Conditions when Classical Mechanics does not
  apply
• very tiny objects (lt atomic sizes)
• objects moving near the speed of light

3
Contact and Field Forces
4
Fundamental Forces

• Types
• Strong nuclear force
• Electromagnetic force
• Weak nuclear force
• Gravity
• Characteristics
• All field forces
• Listed in order of decreasing strength
• Only gravity and electromagnetic in mechanics

5
Newtons First Law

• If no forces act on an object, it continues in
  its original state of motion that is, an object
  at rest remains at rest and an object moving with
  some velocity continues with that same velocity.

6
Inertia

• Is the tendency of an object to continue in its
  original motion

Mass

• A measure of the resistance of an object
  to changes in its motion due to a force
• Measure of inertia in translational motion
• Scalar quantity
• SI units are kg

7
Newtons Second Law

• The acceleration of an object is directly
  proportional to the net force acting on it and
  inversely proportional to its mass.
• F and a are both vectors

8
Units of Force

• SI unit of force is a Newton (N)
• US Customary unit of force is a pound (lb)
• 1 N 0.225 lb

9
Problem 4-6

• A freight train has a mass of 1.5 x 107 kg. If
  the locomotive can exert a constant pull of 7.5 x
  105 N, how long does it take to increase the
  speed of the train from rest to 80 km/h?

10
Solution
vvo at
t7.4 min
11
Gravitational Force

• Mutual force of attraction between any two
  objects
• Expressed by Newtons Law of Universal
  Gravitation

Gravitational constant, G6.67 x 10-11 Nm2/kg2
12
Weight

• The magnitude of the gravitational force acting
  on an object of mass m near the Earths surface
  is called the weight w of the object
• w m g a special case of Newtons
  Second Law
• g can also be found from the Law of Universal
  Gravitation

13
More about weight

• Weight is not an inherent property of an object
• mass is an inherent property of an object
• Weight depends upon location

14
Quick Quiz 4.4
You are talking by interplanetary telephone to a
friend who lives on the Moon. She tells you she
has just won 1 Newton of gold in a contest.
Excitedly, you tell her that you entered Earths
version of the same contest and also won 1 Newton
of gold? Who is richer? (a) Your friend, (b)
you, (c) its a draw.
15
Newtons Third Law

• If two objects interact, the force F12 exerted by
  object 1 on object 2 is equal in magnitude but
  opposite in direction to the force F21 exerted by
  object 2 on object 1.

• F12 may be called the action force and F21 the
  reaction force

16
Quick Quiz 4.1 True or false (a) It is
possible to have motion in the absence of a
force. (b) If an object is not moving, no
external force acts on it.
17
Quick Quiz 4.2 True or false (a) If a
single force acts on an object, the object
accelerates. (b) If an object experiences an
acceleration, a force acts on it. (c) If an
object experiences no acceleration, no external
force acts on it.
18
Some Action-Reaction Pairs

• n and n
• n is the normal force, the force the table exerts
  on the TV
• n is always perpendicular to the surface
• n is the reaction the TV on the table
• n - n

19
More Action-Reaction pairs

• Fg and Fg
• Fg is the force the Earth exerts on the object
• Fg is the force the object exerts on the earth
• Fg -Fg

20
Forces Acting on an Object

• Newtons Law uses the forces acting on an object
• n and Fg are acting on the object (in the figure
  it is the TV set)
• n and Fg are acting on other objects (table)

21
Free Body Diagram

• Diagram must identify all the forces acting on
  the object of interest
• Choose an appropriate coordinate system
• If the free body diagram is incorrect, the
  solution will likely be incorrect

22
Equilibrium

• An object either at rest or moving with a
  constant velocity is said to be in equilibrium
• The net force acting on the object is zero

23
Solving Equilibrium Problems

• Make a sketch of the situation described in the
  problem
• Draw a free body diagram for the isolated object
  under consideration and label all the forces
  acting on it
• Resolve the forces into x- and y-components,
  using a convenient coordinate system
• Apply equations, keeping track of signs
• Solve the resulting equations

24
Problem 4-55
(a) What is the resultant force exerted by the
two cables supporting the traffic light in Figure
P4.55? (b) What is the weight of the light?
25
Conceptual questions

• 1. A ball is held in a persons hand. Identify
  the external forces acting on the ball and the
  reaction on each.
• 4. A rubber ball is dropped onto the floor. What
  force causes the ball to bounce?

26
Newtons Second Law Problems

• Similar to equilibrium except
• Use components
• ax or ay may be zero

27
Conceptual questions

• 3. If a car moves with a constant acceleration,
  can you conclude that there are no forces acting
  on it?
• 18. A truck loaded with sand accelerates along a
  highway. If the driving force on the truck
  remains constant, what happens to the trucks
  acceleration if its trailer leaks sand at a
  constant rate through a hole in its bottom?

28
Solving Newtons Second LawProblems

• Make a sketch of the situation described in the
  problem
• Draw a free body diagram for the isolated object
  under consideration and label all the forces
  acting on it
• If more than one object is present, draw free
  body diagram for each object
• Resolve the forces into x- and y-components,
  using a convenient coordinate system
• Apply equations, keeping track of signs
• Solve the resulting equations

29
Connected Objects

• Apply Newtons Laws separately to each object
• The acceleration of both objects will be the same
• The tension is the same in each diagram
• Solve the simultaneous equations

30
Problem 4-34
Two objects with masses of 3.00 kg and 5.00 kg
are connected by a light string that passes over
a frictionless pulley as in Figure P4.34.
Determine (a) the tension in the string, (b) the
acceleration of each object, and (c) the distance
each object will move in the first second of
motion if both objects start from rest.
31
(T-29.4) N a (3.00 kg)
(49.0-T) N a (5.00 kg)
32
Inclined Planes

• Choose the coordinate system with x along the
  incline and y perpendicular to the incline
• Replace the force of gravity with its components

x
33
Forces of Friction

• When an object is in motion on a surface or
  through a viscous medium, there will be a
  resistance to the motion
• This is due to the interactions between the
  object and its environment
• This is resistance is called the force of friction

34
More About Friction

• Friction is proportional to the normal force
• The force of static friction is generally greater
  than the force of kinetic friction
• The coefficient of friction (µ) depends on the
  surfaces in contact
• The direction of the frictional force is opposite
  the direction of motion
• The coefficients of friction are nearly
  independent of the area of contact

35
Static Friction, s

• Static friction acts to keep the object from
  moving
• If F increases, so does s
• If F decreases, so does s
• s ? µ n

36
Quick Quiz 4.8You press your physics textbook
flat against a vertical wall with your hand.
What is the direction of the friction force
exerted by the wall on the book? (a) downward
(b) upward (c) out from the wall (d) into the
wall.
37
Kinetic Friction

• The force of kinetic friction acts when the
  object is in motion
• k µ n

38
Problem 4-40

• A woman at an airport is towing her 20.0-kg
  suitcase at constant speed by pulling on a strap
  at an angle of ? above the horizontal (Fig.
  P4.40). She pulls on the strap with a 35.0-N
  force, and the friction force on the suitcase is
  20.0 N. Draw a free-body diagram of the suitcase.
  
• (a) What angle does the strap make with the
  horizontal?
• (b) What normal force does the ground exert on
  the suitcase?

39
Solution

• Velocity is constant, Fnet0

Q55.2o
167 N
40
Conceptual questions

• 5. If you push a heavy box that is at rest you
  must exert some force to start its motion.
  However, once the box is sliding, you can apply a
  smaller force to maintain that motion.
• 9. What force causes an automobile to move?
• A propeller driven airplane?
• A rawboat?

41
Terminal Speed

• Another type of friction is air resistance
• Air resistance is proportional to the speed of
  the object
• When the upward force of air resistance equals
  the downward force of gravity, the net force on
  the object is zero
• The constant speed of the object is the terminal
  speed

42
Problem 4-80
A fire helicopter carries a 620-kg bucket of
water at the end of a 20.0-m long cable. When the
helicopter is flying back from a fire at a
constant speed of 40.0 m/s, the cable makes an
angle of 40.0 with respect to the vertical.
Determine the force exerted by air resistance on
the bucket.
43
y
T
R
x
W
Constant velocity means that ax 0 ay 0
Thus Fx 0 Fy 0
44
4-15. Find the tension in each cable supporting
the 600-N cat burglar in Fig. P4.15.  
45
4-49. Find the acceleration experienced by each
of the two objects shown in Figure P4.49 if the
coefficient of kinetic friction between the
7.00-kg object and the plane is 0.250.