FORCE, THE CAUSE OF ACCELERATION; NEWTON’S LAWS OF MOTION
In 1642, several months after Galileo died, Isaac Newton was born. At
age 23, Newton developed his famous laws of motion, which completed the
overthrow of the Aristotelian idea that had dominated the thinking of
the best minds for 2,000 years.
Every acceleration ( change in velocity ) is caused by forces acting on
a body. Conversely, if a body does not accelerate, then the total force
acting on it is zero even if several forces are present. The apparently
simple idea of cause and effect, that forces cause acceleration, didn’t
come easily. It was and still is tempting to think of common phenomena
as having no cause and simple being “the nature of things”. For example,
“Why does water flow downhill?” seems stupid. Yet such question have a
serious answers; in this case, the force of gravity causes water to flow
downhill. The genius of Newton and others was not only in providing
answers to basic questions. But also in simply being curious enough to
ask basic questions.
Force is
defined intuitively as a push or a pull. If an applied force is the
only one thing acting on a body, then the body will accelerate in the
same direction as the force. The strength of the force determines the
magnitude of the acceleration. If several forces act on a body, then its
acceleration is in the same direction as the total force and has
magnitude proportional to the total force.
NEWTON’S LAWS OF MOTION
Galileo
had a major influence in the study of motion. What Newton did was to
write down the relationships between the force and motion in a form that
could be used to predict and describe motion. Those relationships were
found to apply in every circumstance where an experiment could be
performed to test them and came to be known as Newton’s laws of motion.
The First Law
: Inertia (mass). A body rest remain at rest or in motion in a straight
line with a constant velocity unless acted upon by an outside force.
The property of a body that causes it to remain at rest or to maintain a
constant velocity is called inertia. The law was a refinement of
Galileo’s idea --- in the absence of force, a moving object will
continue moving. Galileo considered the tendency of things to resist
change in motion as inertia. Inertia is a measure of how difficult is it to set a body into motion, or if it is already moving, how difficult is it to stop.
The Second Law:
The acceleration produced by forces acting on a body is directly
proportional to and in the same direction as the net external force and
inversely proportional to the mass of the body.
a = Fnet ext / m ==> Fnet ext = ma , m = mass and a = acceleration
Newton’s
Second law gives a precise definition of force that is consistent with
our intuitive notions of a force as a push or a pull. A large force
produces a large acceleration, a large mass requires a large force to
make it accelerate at the same rate as a small mass, and a body will
accelerate in the same direction as the net force on it.
The Third Law :
Action – Reaction. Whenever one body exerts a force on a second body,
the second body exerts a force back on the first that is equal in
magnitude and opposite in direction. This is paraphrase as, “For every
action there is equal and opposite reaction”.
One force is called the action force and the other is the reaction
force. In every interaction, the forces always occur in pairs. The
action and the reaction pair of forces make up the interaction between
two things. We know that forces can cancel when they are equal and act
in the opposite direction on the same object. Even though action and
reaction are equal and oppositely directed, they do not cancel each
other for they are acting on different bodies.
An example is a swimmer that exerts a force on the side of the pool. By
Newton’s third law, the side of the pool exerts a force back on the
swimmer – an external force. If friction is negligible between the
swimmer and the water, she will then move in a direction opposite to the
force she exerted on the side of the pool with an acceleration
proportional to the force she exerted.
Cars accelerate forward by exerting backward forces on the ground. The
reaction force of the ground acts as an external force on the car in the
forward direction.
UNITS OF FORCE
1. Newton – is the force required to give a mass of 1 kilogram an acceleration of 1 m/ s2.
1 newton ( N ) = 1 kg-m/ s2
2. Dyne – is the force required to give a mass of 1 gram an acceleration of 1 cm/ s2.
1 dyne = 1 g-cm/ s2
3. Pound – is the force required to give a mass of 1 slug an acceleration of 1 ft/ s2.
1 lb = 1 slug-ft/ s2 = 4.448 N
WEIGHT, FRICTION, TENSION, AND OTHER CLASSES OF FORCES
The weight
of an object is the gravitational force exerted on it by the earth.
When an object is dropped near the earth’s surface, it is accelerated by
the gravitational force with an acceleration g, thus by Newton’s second
law, the weight w becomes
w = mg. ==> m = w/ g
We see in this equation the relation between mass and weight : Weight is a force proportional to the mass of a body and g is the constant of proportionality. Here, g is taken to be positive,
since the direction of forces are indicated with plus or minus sign.
Weight depends on the location of the object, since the acceleration of
gravity varies with location. As you go higher, g decreases so that
weight also is decreasing. On the moon g = 1/6 ( Earth's g )
Center of gravity. The force of gravity on solids can be considered to act on a single point, called center of gravity (c.g.).For symmetrical objects, c.g. is at its geometric center. For asymmetrical objects, the c.g. is closer to the more massive part of the body. A closer related concept is the center of mass (c.m.), is the point at which all of the mass in a body can be considered to be located.
Newton’s Universal Law of Gravitation.
The law states that there a force of attraction between any two masses
that is proportional to the product of the masses and inversely
proportional to the square of the distance between their centers of
mass.
F = G m1 m2 / r2
where G = Newton’s Universal constant of gravitation
G = 6.67 x 10–11 N . m2/ kg2 , m1 & m2 = masses in kg and
r = distance between the centers of mass in meter.
FRICTION
Friction
is any force that opposes every effort to start to slide or roll one
body over another body. Frictional forces are specially important to us
in our daily lives, for without them we could not walk or hold things
with our hands; cars wouldn’t be able to start or stop; nails and screws
would be useless. Frictional forces are not fundamental forces like
gravity or electromagnetism, but arise as reaction to other applied
forces. Friction is proportional to the force exerted by one substance
on another perpendicular to the surface between them---that is, the normal force (perpendicular force). The mathematical expressions are :
1. f = ukFN , uk is coefficient of kinetic friction , FN is Normal force
2. f = us FN , us is coefficient of static friction
Equation 1 is used for the friction between moving substance and equation 2 for stationary substances.
Coefficient of friction is the ratio of the force of friction f to the normal force, FN.
PRINCIPLES OF FRICTION
1. The force of friction always act in a direction opposite to the
direction of motion, for objects in relative notion --- that is, sliding
or rolling.
2. The frictional force is proportional to the normal (perpendicular ) force between the two surfaces in contact.
3. Frictional force is approximately independent of the area of contact between the surfaces.
4. The frictional force depends on the particular material that make up the surfaces.
* Synovial fluid – a fluid which looks like blood plasma which lubricates the joints and limbs of the body.
ADVANTAGES OF FRICTION
1. Walking would be impossible without friction.
2. Pulley driven machines depend on friction for their operation.
3. Friction prevents belts from slipping off their pulley.
4. Friction between the tires and the road prevents skidding of vehicles.
5. Clutch, bolts and nuts, nails, screws, matches, brakes, etc. depends on friction.
DISADVANTAGES OF FRICTION
1. Wearing out of parts of machines, thus causing extra expenses for maintenance.
2. It causes expansion on machine parts and heat losses due to friction thus reducing the efficiency of machines.
TENSION
A tension
is any force carried by a flexible string, rope, cable, chain, etc.
Because the medium carrying the force is flexible, it can only pull and
can exert no force except along its length. Tension comes from a Latin
word meaning “to stretch thin”. In muscle systems the fibrous cords that carry forces exerted by muscles to other parts of the body are called tendons. Tension is due to the cohesive atomic and molecular electromagnetic forces acting in a string.
For a body suspended on a string with zero or constant speed upward or
downward, the tension is given by T = w = mg. If the body accelerates
downward on a string, the tension is given by T + ma = mg and if the
body has an upward acceleration on a string, the tension is given by T
= mg + ma.
Problems :
1. Determine the weight of a 70 kg person on earth. On the moon, g is 1/6 of the earth’s g, what is the weight of this person ?
2. Determine the mass of a box if a force of 80 N is able to accelerate it at 1.25 m/ s2.
3. Calculate the mass of a flea in grams if its weight is 5 x 10– 6 N.
4. Find the acceleration of a rocket with mass of 1.2 x 10 6 kg if its engine exerts a net force of 2 x 10 6 N.
5.
A 70 kg gymnast climbs on a rope. Determine the tension in the rope if
(a) he climbs at constant speed, (b) he has an upward acceleration of
0.5 m/ s2 ; and (c) he goes downward with a downward acceleration of 0.5 m/ s2.
6. Determine the force of gravitation between the earth and the sun and between the earth and the moon.
mE = 5.99 x 1024 kg , mS = 1.99 x 10 30 kg , mM = 7.36 x 10 22 kg
mE = 5.99 x 1024 kg , mS = 1.99 x 10 30 kg , mM = 7.36 x 10 22 kg
S earth–sun = 149.6 x 109 m , S earth–moon = 3.84 x 108 m,
Radius of the earth = 6.367 x 106 m
Radius of the earth = 6.367 x 106 m
7. A man weighs a fish of mass m on a spring scale attached to the
ceiling of a elevator. Show that if the elevator accelerates in either
direction , the spring scale gives a reading different from the weight
of the fish. What is the reading on the scale if the elevator moves up
or down at constant speed?
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