CHAPTER 4 - FORCES AND NEWTON'S LAWS OF
MOTION
A force is defined as a push or pull. Any physical quantity that
causes a change in speed or direction.
Contact forces require the objects involved to be touching. An
example would be a bat striking a ball.
Action at a distance forces exist regardless of contact. Gravity and
magnetic forces are examples.
Forces are vector quantities with direction and magnitude.
Example - your weight has a magnitude(number of pounds you
weigh) and its direction is always down.
Mass is a measure of the amount of matter of which an object is
composed. Determined by the number of protons, electrons, and
neutrons within the object.
Newton's First Law of motion is called the Law of Inertia. It states:
AN OBJECT MAINTAINS A CONSTANT STATE OF
MOTION(VELOCITY) UNLESS IT IS ACTED UPON BY A
NET FORCE.
This means an object at rest stays at rest and an object moving
continues to do so unless some force acts on it to cause a change.
Remember that net force means the vector sum of all the forces
acting on an object.
Inertia is generally considered to be the measure of an object's
tendency to resist changes of motion when acted upon by a net
force. It is directly related to the mass of the object.
The SI unit of mass is the Kilogram. Remember weight is a force
and is expressed in the unit of force, the Newton.
Inertial reference frame - Newton's Laws are valid.
Non-inertial Reference Frame - Newton's Laws are not valid.
In an inertial reference frame, the origin must be moving at a
constant velocity.(No acceleration)
If the origin is being accelerated, like in a car that suddenly stops,
things begin to move with no apparent force causing them to
accelerate. The earth's surface is an approximation of an inertial
reference frame for small distances(< 1 Km).
Newton's Second Law of Motion describes the relationship among
force, mass, and acceleration. It states:
THE ACCELERATION OF AN OBJECT DEPENDS DIRECTLY
ON THE NET EXTERNAL FORCE APPLIED AND
INVERSELY ON THE MASS OF THE OBJECT.
It says if you increase the net force and keep the mass constant, the
acceleration is larger. It also says if you increase the mass and keep
the force constant, the acceleration decreases.
The equation that results from this is:
F = MA
If mass is in kilograms and acceleration is in meters per second
squared, the resulting force unit is called a Newton(named for Sir
Isaac Newton).
A newton is defined as the force required to accelerate a 1 Kg mass
1 meter per second per second.
When solving problems involving forces acting on an object,
drawing a freebody force diagram is helpful.
Example
Two people are pushing a stalled car that has a mass of 1850 Kg.
One person pushes with a force of 275 newtons and the other with
a force of 395 newtons in the same direction. A frictional force of
560 newtons acts in the direction opposite to that of the forces
supplied by the two people. Find the acceleration of the car.
I will work this one in class.
Since forces are vectors, we can solve problems involving forces
using either method of vector addition. Components of forces
along the X and Y axes may be found and added or the technique
of constructing parallelograms and using the law of cosines and the
law of sines may be used.
Newton's Third Law of Motion is called the Action-Reaction Law.
It states:
FOR EVERY ACTION(FORCE) THERE EXISTS AN EQUAL
AND OPPOSITE REACTION(FORCE).
This means when one object exerts a force on a second object, the
second object exerts an equal and opposite force on the first object.
Example
A 92 kg astronaut pushes on an 11,000kg spacecraft with a force of
36 newtons. Find the acceleration of the astronaut and the
spacecraft.
I will work this one in class.
Types of forces - there are 3 fundamental forces in nature. All
others can be explained in terms of these three. They are:
(1) Gravity - attractive force between objects that have mass.
(2) Strong Nuclear - attractive force between nucleons that are very
close together.
(3) Electroweak - observed as electrical, magnetic, and weak
nuclear forces
Newton's Law of Universal Gravitation
EVERY PARTICLE IN THE UNIVERSE EXERTS AN
ATTRACTIVE FORCE ON EVERY OTHER PARTICLE IN
THE UNIVERSE. THIS FORCE IS DIRECTLY
PROPORTIONAL TO THE PRODUCT OF THE TWO MASSES
AND INVERSELY PROPORTIONAL TO THE SQUARE OF
THE DISTANCE BETWEEN THEM.
The equation that describes this concept is:
F = GM1M2
R2
Where F is the gravitational force, G is Newton's Universal
Gravitation Constant, M1 and M2 are the two masses, and R is the
distance between the centers of mass of the two objects. If the two
objects are homogeneous, the centers of mass correspond to their
geometrical centers.
Any of the variables in the equation can be found if the rest are
known.
Example
Find the magnitude of the gravitational force acting on each
particle if one mass is 12 kg, the other one is 25 kg and they are 1.2
meters apart.
I will work this one in class.
Weight is defined as the gravitational force exerted on an object
when it is near another very large object.
The SI unit of weight is the Newton(N).
Newton's Universal Law of Gravitation can be used to calculate
the weight of an object near the earth by using the mass of the
earth as M1 and the distance from the center of the earth as R.
Example
The mass of the Hubble Space Telescope is 11,600 kg. Find its
weight (1)on the surface of the earth and (2)in its orbit at 598 km
above the surface of the earth.
The relationship between weight and mass can also be written as
the product of mass and acceleration.
Using Newton's Second Law,
F = MA
In the case of gravitational acceleration, we write:
A=g
F = Mg
On the surface of the earth, g = 9.80 m/s2. It is slightly different at
different places on the surface of the earth and can be considerably
different on other planets and moons.
It can be calculated from Newton's Universal Law of Gravitation
by using the mass of the earth for M1 and the radius of the earth for
R. M2 is not included since we are calculating an acceleration, not
a force.
The Normal Force and Friction
Newton's Third Law tells us when a contact force is exerted on one
object by another, the second object exerts an equal and opposite
force on the first object.
The component of this force that is perpendicular to the surfaces in
contact is called the Normal Force.
The Normal Force is found by adding vectorially the normal
components of all the other forces acting on the object.
(1) If an object is resting on a horizontal surface, Fn = Mg
(2) If an object on a horizontal surface is being partly lifted by
another force, Fa, then Fn = Mg - Fa.
(3) If an object on a horizontal surface is being pushed down by
another force, Fa, then Fn = Mg + Fa
Apparent Weight is equal to the Normal force acting on the object.
This concept is usually applied in the case of an object being
accelerated up or down while in contact with a rope or floor.
If the object is accelerated up, the apparent weight equals the sum
of the actual weight and the accelerating force.
If the object is accelerated down, the apparent weight equals the
actual weight minus the equivalent of the accelerating force.
This apparent weight is equal to the tension in a supporting rope or
cable.
Friction - Static and Kinetic
Friction is a force that always opposes motion. The two types we
are considering are called Static(friction when the two surfaces
involved are not moving) and Kinetic(they are moving)
Friction exists because rough surfaces interlock and reduce or stop
motion. Even if surfaces are polished as smooth as possible, other
factors play a role. These forces are the dipole-dipole interaction
and the electron dispersion effect.
The dipole-dipole interaction depends on regions of molecular
polarity and the electron dispersion effect involves rearrangement
of electrons into lower energy states when the molecules are close.
Friction is very often undesirable and is reduced by using
lubricants, smoothing surfaces in contact or changing sliding
friction to rolling or fluid.
There are cases where friction is desirable or even necessary as in
the case of tires, fingerprints, or walking.
In the case of friction involving solids, frictional force depends on
the nature of the two surfaces and the force pressing the two
surfaces together.
The equation is:
Fs = μsFn
Where Fs is the magnitude of the frictional force, μs is the
coefficient of friction for the two surfaces involved, and Fn is the
normal force pressing the two surfaces together.
Fs is referred to as the maximum static frictional force since any
force less than that will not cause motion of the object
experiencing the frictional force.
Example
A sled is resting on a horizontal surface. The coefficient of static
friction between the sled and the surface is .350. The total mass of
the sled is 38 kg. Find the maximum horizontal force that can be
applied to the sled without causing it to move.
I will work this one in class.
If the two objects in contact are moving relative to each other, the
frictional force is called the kinetic frictional force.
The same equations apply with one slight change:
Fk = μkFn
The coefficient of kinetic friction is always less than the coefficient
of static friction.
Example
A sled travels at 4.00 m/s along a horizontal stretch of snow. The
coefficient of kinetic friction is 0.0500. How far does it go before it
stops?
I will work this one in class.
These equations only work for conditions that do not cause a
change in the nature of the two surfaces in contact. If one surface
begins to melt or change temperature significantly, the coefficient
of friction will change.
Tension in a rope is a stretching force. If a force is applied at one
end of a rope, the same force can be applied by the other end of a
rope on an attached object. The direction of the tension force is
always in the same direction as that of the rope.
Equilibrium occurs when the vector sum of the forces acting on an
object is zero. If the forces are broken into perpendicular
components, the sum of forces in each of those directions must
also be zero.
Since the net force is zero, the acceleration of the object must also
be zero. Any object in equilibrium maintains a constant speed and
direction. The converse is also true. If an object maintains a
constant velocity, then it is in equilibrium.
The equations for equilibrium are:
(1) Σ Fx = 0 and (2) Σ Fy = 0
Example
A 30 kg sled is being pulled across a level surface at a constant
velocity by a rope angled at 30 degrees above the horizontal. If the
force applied to the rope is 80 newtons, find the coefficient of
friction between the sled and the surface.
I will work this one in class.
When equilibrium does not exist, there is a net force and the
acceleration of the object can be calculated using Newton's Second
Law.
a = F/M where a = acceleration, F = net force and M = mass of
the object. The acceleration will be in the same direction as the net
force.
Example
A skateboarder is skating down a ramp 6.0 m long and angled at 18
degrees with respect to the horizontal. If the initial speed at the top
is 2.6 m/s and there is no friction,, find the final speed at the
bottom.
I will work this one in class.
P 125 Questions 1,2,4,6,8,10,11,15,16,18,20,21,22,26
P 127 Problems 3, 5, 9, 11, 19, 23, 27, 29, 35, 37, 39, 43, 47, 49,
51, 53, 55, 57, 59, 63, 67, 69, 77,91