Download In the absence of external forces, when viewed from an inertial

Lecture 2
The Laws of Motion or Laws of Newton
1. Concept of Force.
1. Force is associated with the body till it is in motion.
2. When a body is at rest the force acting on it is zero.
3. If the net force exerted on an object is zero, the acceleration of the object
is zero and its velocity remains constant.
4. Force is always in the same direction as the velocity of the body.
5. If the velocity is changing then the force is also changing.
6. Centripetal force and centrifugal force both act on the body moving uniformly in a circle.
7. The action-reaction forces act on the same body.
8. The product of mass and acceleration is a force.
9. Only animate things like people and animals exert forces; passive ones like tables, floors do
not exert forces.
10. A force applied by, say a hand, still acts on the object even after the object leaves the hand.
Some examples of applied forces. In each case a force is exerted on the object within the boxed
area. Some agent in the environment external to the boxed area exerts a force on the object.
Contact forces involve physical contact between two objects. Field forces, do not involve
physical contact between two objects but instead act through empty space. When examined at the
atomic level, all the forces we classify as contact forces turn out to be caused by electric (field)
forces. fundamental forces in nature are all field forces: (1) gravitational forces between objects,
(2) electromagnetic forces between electric charges, (3) nuclear forces between subatomic
particles, and (4) weak forces that arise in certain radioactive decay processes.
Forces have been experimentally verified to behave as vectors, therefore you must use the rules
of vector addition to obtain the net force on an object.
Unit of Force
The SI unit of force is the newton, which is defined as the force that, when acting on an object of
mass 1 kg, produces an acceleration of 1 m/s2. From this definition and Newton’s second law,
we see that the newton can be expressed in terms of the following fundamental units of mass,
length, and time:
1 N = 1 kgm/s2
Newton’s first law of motion
Newton’s first law of motion, sometimes called the law of inertia, defines a special set of
reference frames called inertial frames. This law can be stated as follows:
If an object does not interact with other objects, it is possible to identify a reference frame in
which the object has zero acceleration.
Such a reference frame is called an inertial frame of reference. Any reference frame that moves
with constant velocity relative to an inertial frame is itself an inertial frame.
Given our assumption of observations made from inertial reference frames, we can pose a more
practical statement of Newton’s first law of motion:
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
(that is, with a constant speed in a straight line).
An object at rest will remain at rest unless acted on by an unbalanced force. An object in
motion continues in motion with the same speed and in the same direction unless acted
upon by an unbalanced force.
In simpler terms, we can say that when no force acts on an object, the acceleration of the object
is zero. If nothing acts to change the object’s motion, then its velocity does not change. From the
first law, we conclude that any isolated object (one that does not interact with its environment) is
either at rest or moving with constant velocity. The tendency of an object to resist any attempt to
change its velocity is called inertia.
Mass
Mass is that property of an object that specifies how much resistance an object exhibits to
changes in its velocity. The SI unit of mass is the kilogram. The greater the mass of an object, the
less that object accelerates under the action of a given applied force.
Mass is an inherent property of an object and is independent of the object’s surroundings and of
the method used to measure it. Also, mass is a scalar quantity and thus obeys the rules of
ordinary arithmetic.
Mass should not be confused with weight. Mass and weight are two different quantities. The
weight of an object is equal to the magnitude of the gravitational force exerted on the object and
varies with location.
Newton’s Second Law
Newton’s second law answers the question of what happens to an object that has a nonzero
resultant force acting on it.
Acceleration is produced when a force acts on a mass. The greater the mass (of the object
being accelerated) the greater the amount of force needed (to accelerate the object).
What does this mean?
Everyone unconsiously knows the Second Law. Everyone knows that heavier objects require
more force to move the same distance as lighter objects.
Second Law gives us an exact relationship between force, mass, and acceleration. It can be
expressed as a mathematical equation:
(1)
In both the textual and mathematical statements of Newton’s second law above, we have
indicated that the acceleration is due to the net force #F acting on an object. The net force on an
object is the vector sum of all forces acting on the object. In solving a problem using Newton’s
second law, it is imperative to determine the correct net force on an object. There may be many
forces acting on an object, but there is only one acceleration.
(2)
Force does not cause motion. We can have motion in the absence of forces, as described in
Newton’s first law. Force is the cause of changes in motion, as measured by acceleration.
Newton’s Third Law
A general principle of critical importance known as Newton’s third law:
If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and
opposite in direction to the force F21 exerted by object 2 on object 1:
(3)
Newton’s third law. (a) The force F12 exerted by object 1 on object 2 is equal in magnitude
and opposite in direction to the force F21 exerted by object 2 on object 1.
The third law, which is illustrated in Figure 5.5a, is equivalent to stating that forces always
occur in pairs, or that a single isolated force cannot exist. The force that object 1 exerts on object
2 may be called the action force and the force of object 2 on object 1 the reaction force. In
reality, either force can be labeled the action or reaction force. The action force is equal in
magnitude to the reaction force and opposite in direction. In all cases, the action and reaction
forces act on different objects and must be of the same type.
Applying Newton’s Laws
The following procedure is recommended when dealing with problems involving
Newton’s laws:
• Draw a simple, neat diagram of the system to help conceptualize the problem.
• Categorize the problem: if any acceleration component is zero, the particle is in equilibrium in
this direction and ΣF = 0. If not, the particle is undergoing an acceleration, the problem is one of
nonequilibrium in this direction, and ΣF = ma.
• Analyze the problem by isolating the object whose motion is being analyzed. Draw a free-body
diagram for this object. For systems containing more than one object, draw separate free-body
diagrams for each object. Do not include in the free-body diagram forces exerted by the object
on its surroundings.
• Establish convenient coordinate axes for each object and find the components of the forces
along these axes. Apply Newton’s second law, #F " ma, in component form. Check your
dimensions to make sure that all terms have units of force.
• Solve the component equations for the unknowns. Remember that you must have as many
independent equations as you have unknowns to obtain a complete solution.
• Finalize by making sure your results are consistent with the free-body diagram. Also check the
predictions of your solutions for extreme values of the variables. By doing so, you can often
detect errors in your results.