Chapter 4
Dynamics: Newton’s Laws of
Motion
Units of Chapter 4
• Force
• Newton’s First Law of Motion
• Mass
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion
• Weight—the Force of Gravity; and the Normal Force
• Solving Problems with Newton’s Laws: Free-Body Diagrams
• Problem Solving—A General Approach
What is force and the effects of force?
4-1 Force
A force is a push or pull.
An object at rest needs a force to get it moving; a moving object
needs a force to change its velocity.
4-1 Force
Force is a vector, having both magnitude and direction. The
magnitude of a force can be measured using a spring scale.
Definition (FORCE) A force is a push or a pull on a body.
A force can be transmitted to a body by contact, or by a field
(action-at-a-distance).
Contact forces arise from physical contact between two objects.
Field forces (action-at-a-distance forces) do not require contact
between objects. Examples include gravitational, electrostatic, and
magnetic forces.
In nature there are two general types of forces,
fundamental and non-fundamental.
Fundamental Forces
1. Gravitational force
2. Strong Nuclear force
3. Electroweak force
Examples of nonfundamental forces:
friction
tension in a rope
normal or support forces
Examples of contact and Field forces
Effects of a force
•
•
•
•
•
Can change the direction of a moving object
Can increase or decrease the speed of a moving object
Can make a stationary object to start moving
Can cause deformation on an object
Can stop a moving object
Sir Isaac Newton
• 1642-1727
• Formulated the basic
concepts and laws of
mechanics
• Calculus
• Light and optics
4-2 Newton’s First Law of Motion
It may seem as though it takes a force to keep an object moving.
Push your book across a table—when you stop pushing, it stops
moving.
But now, throw a ball across the room. The ball keeps moving after
you let it go, even though you are not pushing it any more. Why?
It doesn’t take a force to keep an object moving in a straight line—
it takes a force to change its motion. Your book stops because the
force of friction stops it.
Newton’s First Law of motion
• An object will maintain its state of rest, or motion at
constant speed along a straight line, unless compelled to
act otherwise by a non-zero net external force.
• Newton’s first law of motion is also called the law of inertia
• Inertia is tendency of an object to maintain its state of
motion or state of rest.
• The mass of an object is a quantitative measure of inertia
(SI Unit of Mass: kilogram)
NOTE:
Net force is the vector sum of all external forces acting on an
object. All the forces acting on an object are added as vectors to
find the net force acting on the object
External forces results from the interaction between the object
and its environment.
Internal forces originate within the object itself, and cannot
change the object’s velocity.
The net force on an object is the vector sum
of all forces acting on that object.
The SI unit of force is the Newton (N)
Example: Two forces act on body as shown in the
figures. Calculate the net force and describe the body’s
state of motion in each case.
4-2 Newton’s First Law of Motion
Conceptual Example 4-1: 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?
Mass
Mass is the measure of inertia of an object, sometimes
understood as the quantity of matter in the object. In the SI
system, mass is measured in kilograms.
Mass is not weight.
Mass is a property of an object. Weight is the force exerted
on that object by gravity.
If you go to the Moon, whose gravitational acceleration is
about 1/6 g, you will weigh much less. Your mass, however,
will be the same.
Newton’s Second Law of motion
When a net external force acts on an object, the resultant acceleration
is directly proportional to the net force and inversely proportional to
the mass of the object.
Note: When there is no net force on an object, its acceleration is
zero, which means that velocity is constant.
4-4 Newton’s Second Law of Motion
Newton’s second law is the relation between acceleration and force.
Acceleration is proportional to force and inversely proportional to
mass.
It takes a force to change either the
direction or the speed of an object.
More force means more acceleration;
the same force exerted on a more
massive object will yield less
acceleration.
4-4 Newton’s Second Law of Motion
Force is a vector, so
is true along each coordinate axis.
The unit of force in the SI system
is the newton (N).
Note that the pound is a unit of
force, not of mass, and can
therefore be equated to newtons
but not to kilograms.
Free Body 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
Example 4-1:The figure below shows a car being pushed on a
horizontal frictionless road.
(a)Calculate the resultant force on the car.
(b)If the mass of the car is 1850 kg, calculate its acceleration.
12θ
A free-body-diagram is a diagram that represents the object
and the forces that act on it.
4.2.Estimate the net force needed to accelerate
(a) a 1000-kg car at ½ g
(b) a 200-g apple at the same rate.
4-4 Newton’s Second Law of Motion
Example 4-3: Force to stop a car.
What average net force is required to bring a 1500-kg car to rest
from a speed of 100 km/h within a distance of 55 m?
4-5 Newton’s Third Law of Motion
Any time a force is exerted on an object, that force is caused by
another object.
Newton’s third law:Whenever one object exerts a force on a
second object, the second exerts an equal force in the opposite
direction on the first.
4-5 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.
4-5 Newton’s Third Law of Motion
Rocket propulsion can also be explained using Newton’s third law: hot
gases from combustion spew out of the tail of the rocket at high
speeds. The reaction force is what propels the rocket.
Note that the rocket
does not need
anything to “push”
against.
4-5 Newton’s Third Law of Motion
Conceptual Example : What exerts the force to move a
car?
Response: A common answer is that the engine makes
the car move forward. But it is not so simple. The
engine makes the wheels go around. But if the tires are
on slick ice or deep mud, they just spin. Friction is
needed. On firm ground, the tires push backward
against the ground because of friction. By Newton’s
third law, the ground pushes on the tires in the opposite
direction, accelerating the car forward.
4-5 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.
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.
Newton's third law implies that forces in nature always
exist in pairs (called action and reaction), i.e. a single
isolated force cannot exist;
• The action force equals the reaction force in
magnitude, but opposite in direction. F action = - F reaction
4-6 Weight—the Force of Gravity
Weight is the force exerted on an object by gravity. Close to
the surface of the Earth, where the gravitational force is
nearly constant, the weight of an object of mass m is:
where
Mass: is a measure of the quantity of matter in an object, i.e. it’s a
quantitative measure of inertia. Weight is the magnitude of the gravitational
force acting on the mass of an object. Weight, 𝑤=𝑚g
4. An object weighs 20N on Earth (𝑔=9.8𝑚/𝑠2). What is
the weight of the same object on a planet whose gravity
is 1.7 𝑚/𝑠2?
−3
5.A 15-g bullet is fired from a rifle. It takes 2.5 × 10 𝑠 for
the bullet to travel the length of the barrel, and it exits the
barrel with a speed of 715 m/s. Assuming that the
acceleration of the bullet is constant, find the average net
force exerted on the bullet.
6. Two forces, F1 and F2 act on the 7.00-kg block shown in
the drawing. The magnitudes of the forces are F1 = 59.0 N
and F2 = 33.0 N. What is the horizontal acceleration
(magnitude and direction) of the block?
F1 = 59.0 N
70.0 0
7.00 kg
F2 = 33.0 N
7. Only two forces act on an object (mass = 3.00 kg), as in
the drawing. Find the magnitude and direction (relative to
the x axis) of the acceleration of the object.
+Y
F2 = 60.0 N
45.00
3.00 kg
F1 = 40.0 N
9.A 1580-kg car is traveling with a speed of 15.0 m/s.
What is the magnitude of the horizontal net force that
is required to bring the car to a halt in a distance of
50.0 m?