Week 2 Overview Last week, we studied the relationship between acceleration, velocity, displacement, and time. Acceleration in an object is caused by the force acting on it. This week, we'll study the relationship between force and acceleration. Central to this study are the laws of motion that Isaac Newton discovered in the 17th century. You must have observed in daily life that when you apply brakes to a car, it takes some time before the car stops completely. The speed with which a train moves depends on the amount of force applied by the engine. A ball thrown at a wall bounces back. Newton's laws help you understand the motion of day-to-day objects and explain all this phenomena. These laws can also help you create realistic graphic animations! Have you ever walked on slippery surfaces? If so, you would have realized how difficult it is to walk on them. Slippery surfaces have less friction, which makes it difficult to walk. In fact, surface transportation would be impossible without friction. This week, we take a closer look at this important force. We will use Newton's laws to analyze problems involving friction. Newton’s First Law What are Forces? Forces are the result of the interaction between bodies. In simple words, a force is the push or pull acting on an object. For example, you exert a force on a rope to pull an object, and the rope pulls the object.    Here, we need a transition between the definition of forces and Newton’s Laws. We also need a couple of examples of how to draw a force diagram. The Law of Inertia Newton's first law of motion explains the relation between the force applied on an object and its motion. The law states that: An object continues to remain in a state of rest or of uniform motion in a straight line unless compelled by an external force to act otherwise. This means that an object prefers to remain in a state of rest or uniform motion; in order to change the state it's in you need to apply force to it. Further, an object will always resist the force applied to it. The property of an object to resist an external force is called inertia, and for this reason, Newton's first law is called the law of inertia. If you slide an object on a smooth floor with a given speed, the distance it moves depends upon the friction between the object and the floor. The smoother the floor, the greater the distance traveled by the object. The object eventually stops because of the external force of friction. A force is required to change the velocity of a body. To understand this statement first recall from your study of kinematics that velocity is a vector with a magnitude (speed) and a direction. In the absence of a force, both speed and direction are constant. When a force acts on an object, it changes the speed, direction, or both of the objects. There is no basic difference between an object at rest and an object in uniform motion; rest and uniform motion are relative terms. An object at rest with respec.

1. Week 2 Overview
Last week, we studied the relationship between acceleration,
velocity, displacement, and time. Acceleration in an object is
caused by the force acting on it. This week, we'll study the
relationship between force and acceleration. Central to this
study are the laws of motion that Isaac Newton discovered in
the 17th century.
You must have observed in daily life that when you apply
brakes to a car, it takes some time before the car stops
completely. The speed with which a train moves depends on the
amount of force applied by the engine. A ball thrown at a wall
bounces back. Newton's laws help you understand the motion of
day-to-day objects and explain all this phenomena. These laws
can also help you create realistic graphic animations!
Have you ever walked on slippery surfaces? If so, you would
have realized how difficult it is to walk on them. Slippery
surfaces have less friction, which makes it difficult to walk. In
fact, surface transportation would be impossible without
friction. This week, we take a closer look at this important
force. We will use Newton's laws to analyze problems involving
friction.
Newton’s First Law
What are Forces?
Forces are the result of the interaction between bodies. In
simple words, a force is the push or pull acting on an object.
For example, you exert a force on a rope to pull an object, and
the rope pulls the object.
Here, we need a transition between the definition of forces and

2. Newton’s Laws. We also need a couple of examples of how to
draw a force diagram.
The Law of Inertia
Newton's first law of motion explains the relation between the
force applied on an object and its motion.
The law states that:
An object continues to remain in a state of rest or of uniform
motion in a straight line unless compelled by an external force
to act otherwise.
This means that an object prefers to remain in a state of rest or
uniform motion; in order to change the state it's in you need to
apply force to it. Further, an object will always resist the force
applied to it. The property of an object to resist an external
force is called inertia, and for this reason, Newton's first law is
called the law of inertia.
If you slide an object on a smooth floor with a given speed, the
distance it moves depends upon the friction between the object
and the floor. The smoother the floor, the greater the distance
traveled by the object. The object eventually stops because of
the external force of friction.
A force is required to change the velocity of a body. To
understand this statement first recall from your study of
kinematics that velocity is a vector with a magnitude (speed)
and a direction. In the absence of a force, both speed and
direction are constant. When a force acts on an object, it
changes the speed, direction, or both of the objects.
There is no basic difference between an object at rest and an
object in uniform motion; rest and uniform motion are relative
terms. An object at rest with respect to one observer may have a
uniform velocity with respect to another observer.

3. Newton’s Second and Third Laws (1 of 2)
Newton's Second Law
Newton second law states that:
The acceleration of an object is proportional to the applied
force and takes place in the direction of the impressed force.
An object may experience a number of forces at any instant; one
of them is the gravitational force, which always acts on an
object in addition to other forces. The vector sum of all the
forces acting on an object at any instant is known as the net
force.
According to Newton's second law, acceleration is proportional
to the net force acting on an object and takes place in the
direction of the net force. Therefore, if the force on an object is
doubled, the acceleration will also be doubled. The relation
between the force and acceleration of an object depends on the
mass of the object; when the mass increases, the same force
produces less acceleration.
Mathematically, Newton's second law is expressed as:
F = ma
Where:
F = net force acting on an object
m = Mass of the object
a = acceleration of the object
Newton's second law gives us a quantitative measure of the
acceleration of an object when a force acts on it. While
calculating the acceleration caused by a force, remember that
the direction of acceleration is always in the direction of the
force and its magnitude depends on the magnitude of the force
and the mass of the object.

4. Because force and acceleration are vectors, Newton's second
law can be applied in any direction you want. The sum of the
components of all forces in a given direction equals the product
of the mass and the acceleration component in that direction.
Newton's second law is also used to define the unit of force,
Newton (N), as the force required to accelerate an object with a
mass 1 kg by 1 m/s2. Thus, 1 N = 1 kgm/s2.
Inertial Reference Frames
An important consideration while applying Newton's first and
second laws is that these laws can be applied only by observers
who are themselves not accelerating. For example, a person
sitting in an accelerating car or riding a roller coaster cannot
apply Newton's first or second law. The person should be
located in another frame of reference where he is not
experiencing the force being analyzed. Frames of reference
where Newton's laws are applicable are called inertial reference
frames.
Newton’s Second and Third Laws (2 of 2)
Newton's Third Law
Now let's study about Newton's third law. It states that:
To every action (force) there is an equal and opposite reaction
(force).
According to this law, all forces occur in pairs, called action-
reaction pairs. When one object exerts a force on another
object, the second object exerts an equal and opposite force on
the first object.
It is important to note that the action and reaction forces act on
different objects. For example, if you push a car (action), the

5. car in turn pushes you back (reaction). Because the action and
reaction forces are not acting on the same objects, they don't
cancel each other. If action and reaction were to act on the same
object, then all the forces on an object would be in exact
balance, and the object would never accelerate.
Application of Newton’s Laws (1 of 3)
Newton's laws of motion can be used to solve a wide variety of
problems that involve force and motion. Let's apply Newton's
laws to find the acceleration produced by a force in a
wheelbarrow.
Application of Newton’s Laws (2 of 3)
Imagine a statue resting on a table. It is acted upon by various
objects, and in turn, it reacts on those objects. Let's use
Newton's laws to analyze the forces acting on the statue.
What are the forces acting on the statue? One of the forces is
the pull that the Earth exerts on the statue called the weight of
the statue. If the table suddenly disappears, the statue will fall
down with an acceleration of 9.8 m/s2 until it hits the floor and
perhaps shatters to pieces. However, the table prevents this
from happening.
The table must be exerting an upward force on the statue equal
to the weight of the statue, given by Newton's second law, F =
mg applied in the vertical direction. Because the statue is not
moving either up or down, it does not have acceleration either
upward or downward. Therefore, there is no net force on the
statue. The weight of the statue is acting downward, so the table
must be exerting an equal force upward.
Is the force exerted by the table on the statue the reaction to the
weight of the statue? No, it is not. Both these forces act on the
statue and cannot be an action-reaction pair.

6. Recall that the weight of the statue is the force with which the
Earth attracts the statue. The reaction force is the force with
which the statue attracts the Earth.
Then what about the reaction force to the force exerted by the
table? Because the statue and the table are in contact, the table
pushes up on the statue, and the statue presses down on the
table with an equal force. We have already shown that the
upward force exerted by the table is equal in magnitude to the
weight of the statue. Therefore, the statue presses down on the
table with a force equal to the weight of the statue. This force is
called the normal force, FN, as it is always perpendicular to the
surface, or normal to the surface.
Application of Newton’s Laws (3 of 3)
Often when analyzing how forces act on an object, it is helpful
to draw a free body diagram. A free body diagram is a drawing
showing all of the forces acting on the object, as well as the net
force if applicable. For the previous example of a statue resting
on a table, we would draw the following free body diagram:
Friction
Friction forces arise when objects rub against each other.
Friction acts parallel to the surface and opposes motion. Even
though friction opposes motion, it doesn't always play a
negative role. Without friction, all forms of surface transport
including walking and running will be impossible.
Experiments show that there are two types of friction forces:

7. · Static friction
· Kinetic friction
Let's look at each one of them.
Static Friction
It is a common experience that if a heavy object such as a crate
is pulled or pushed, the object does not begin to move unless
the force applied reaches a critical value. Below this critical
value, a static friction force prevents motion. The static friction
adjusts itself so that it is equal to the applied force up to a limit.
If the applied force exceeds this limit, the static friction does
not increase any further and the body starts to slide.
The limiting value of static friction is found from experiments
to be directly proportional to the force with which the object is
pressing the floor, in other words, the normal force. For a
horizontal surface, the normal force, FN, is equal to the weight,
FG, of the object. The maximum static friction can be expressed
as:
FFric = μSFN
The constant μ does not have any units because it is the ratio of
two forces. μ is called the coefficient of friction. It represents
how the force of friction depends upon the “roughness” of the
surfaces in contact. The coefficient of friction is different for
different combinations of surfaces. Here, we’ve labeled it μS to
indicate that it is the coefficient of static friction.
Let's solve an example based on the above equation.
Drag

8. When you swim, you feel the resistance of the water to your
motion. Friction forces are also present when a body moves in a
fluid. This force is called the drag force. Of particular interest
is the motion of bodies in air. Air too is a fluid and offers
resistance to motion. When blunt objects such as a ball move
through the air, the drag force is found to be proportional to the
square of its speed. This means that the drag increases by four
times if the speed is doubled. As a result, high-speed vehicles
are given a sleek shape to reduce the cross-section area A so
that drag is reduced.
Terminal Velocity
Why does a raindrop have such a low speed of about 7 m/s
considering that it is falling from such a height? If the drop is
assumed to fall from a height of 500 m and accelerates all the
way down, it would have a speed of 225 mi/h. It would be
dangerous to go out in the rain! The answer is that drag forces
limit the speed of falling drops.
As the drops fall, they initially accelerate due to their weight,
but as the velocity increases, drag also increases as the square
of the velocity. When the drop reaches a velocity of 7 m/s, the
drag force is equal to the weight of the drop. From Newton's
second law (or first law) there is no net force on the drop and
the drop continues to move at 7 m/s thereafter. This constant
velocity is called the terminal velocity of the drop, and it is
different for different objects. A skydiver in a free fall has a
terminal velocity of about 60 m/s. The skydiver can vary the
velocity within limits by varying the cross-sectional area he
offers perpendicular to the direction of motion.
A parachute also works on the principle of terminal velocity. By
offering a large cross-sectional area, the parachute quickly
attains a terminal velocity of a few meters per second and safely
brings the parachutist down to the ground.

9. Week 2 Summary
This week, you studied about Newton's laws of motion.
Newton's first law is about inertia, which resists the force
applied on an object if the direction of the force is opposite to
the direction of motion of the object. Newton's second law, F =
ma, provides a relationship between force, mass, and
acceleration of an object. Newton's third law states that all
forces act in pairs, called action-reaction pairs. Use the
knowledge gained during the week to understand and solve
problems related to force, mass, acceleration, and friction in
real life.