LECTURE 6: FORCE
Prof. Flera Rizatdinova
Example 2 (From lecture 5)
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
A boy whirls a stone in a horizontal circle of radius of
1.5 m and height 2m above level ground. The string
breaks, and the stone flies off horizontally and strikes
ground after traveling a horizontal distance of 10 m.
What is the magnitude of the centripetal acceleration
of the stone during the circular motion?
Solution: y y0 12 gt 2 y 0; y0 2m
t
2 y0 / g
R
v0 x t
v0 x
R/t
R / 2 y0 / g
R (range) = 10 m; v=v0x, so v = 15.8 m/s
a
v2 r
a 15.82 1.5 166.7m / s 2
Nonuniform Circular Motion
3
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If an object moves in a
circular path but its speed
changes, then this is
nonuniform circular motion.
If an object moves in a circular path but its speed changes,
then this is nonuniform circular motion.
Radial acceleration keeps the object in circular motion
The parallel component of acceleration is called tangential
acceleration (because it is tangent to the circle) – it changes
the speed but not the direction.
Force and Motion
Chapter 4
Dynamics
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
We would like to be able to explain why motion of
the object is changing – this is subject of dynamics.
Examples of changing of motion:
 Stopping
 Starting
the motion
 Speeding up
 Slowing down
Sir Isaac Newton
From Wikipedia:
Sir Isaac Newton, (4 January 1643 – 31 March
1727 [OS: 25 December 1642 – 20 March 1726])
was an English physicist, mathematician, astronomer,
natural philosopher, alchemist, and theologian and one
of the most influential men in human history. His
Philosophiæ Naturalis Principia Mathematica, published
in 1687, is considered to be the most influential book
in the history of science. In this work, Newton described
universal gravitation and the three laws of motion,
laying the groundwork for classical mechanics, which
dominated the scientific view of the physical Universe
for the next three centuries and is the basis for modern
engineering.
Force
Force: push or pull
Force is a vector – it has magnitude and direction
Forces we know from
everyday’s life
1) Gravity
2) Friction
3) Restoring force (springs)
4) Tension
5) … (a lot of others)
So, what is the force?
Newton’s first law
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
Newton reasoned that a moving object possessed
some “quantity of motion” that, in effect, kept it
going. But what was this quantity?
Could it be force? No! Galileo showed that the
ancient idea that force is needed to keep something
moving is wrong.
Newton’s First Law
Law of Inertia (discovered by Galileo)
A body in uniform motion remains in uniform motion,
and a body at rest remains at rest, unless acted upon
by a nonzero net force.
That is, if the forces on an object cancel the object’s
motion will not change.
Newton’s First Law
Newton concluded that the appropriate “quantity of
motion” is momentum
p mv
the product of the mass and the velocity.
Note that like velocity, momentum is a vector.
Newton’s Second Law
Law of Motion
The rate at which a body’s momentum changes is equal
to the net force acting on the body:
Fnet
dp
dt
Newton’s Second Law
Fnet
dp
dt
d (mv )
dt
dm
dv
v m
dt
dt
Newton’s 2nd law of motion becomes much
simpler if the mass is constant:
Fnet
dv
m
dt
ma
Example 1
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
F
F
A 1100 kg car traveling at 27 m/s starts to decelerate and
comes to a complete stop in 578 m. What is the average
braking force acting on the car?
Solution:
ma; v 2f
vi2 2a
1100 0.63
x
693N
a
vi2 (2 x)
0.63 m s 2
Clicker question
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An object is moving to the right in a straight line. The net force
acting on the object is also directed to the right, but the
magnitude of the force is decreasing with time. The object will
1) continue to move to the right, with its speed increasing with
time
2) continue to move to the right, with its speed decreasing with
time
3) continue to move to the right with constant speed
4) stop and then begin moving to the left
F = ma
v
Example 2
There are two forces on 2 kg box in the overhead view, but
only one is shown. For F1= 20N, a=12 m/s2 and =30°, find
the second force

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

F1
In a unit-verctor notation
Its magnitude

a
Solution:

Fnet
 

F1 F2 ; ma


ma1 ma2

a
a2 x
ax
ay
a1
a1x ; a2 y
ax
a sin ; a y
a2 x
12 sin 30
F2 x
ma2 x
a1 y ; a1x
a cos ;
20 / 2
8N ; F2 y
 
a1 a2
a1 y
0
Now we can calculate components of a2
4m/s 2 ; a2 y
20.8N
10.4m/s 2
Magnitude:
F2
Finally:
F22x
Fyx2
21.9 N
Inertia
We can rewrite Newton’s 2nd law for constant
mass as follows:
a
Fnet
m
This shows that mass is a measure of a body’s
resistance to changes in motion, that is, mass
measures a body’s inertia. The greater the
mass, the greater the inertia.
Inertia
If no force acts on an object, an inertial
reference frame is any frame in which there
is no acceleration on an the object.
In (a) the plane is flying horizontally at
constant speed, and the tennis ball does not
move horizontally.
In (b) the pilot suddenly opens the throttle
and the plane rapidly gains speed, so that
the tennis ball accelerates toward the back
of the plane.
Inertia is the tendency of mass to resist
acceleration, so that a force must be
supplied to overcome inertia and produce
acceleration.
Inertia
The SI unit of force is defined as follows:
a force of 1 newton (N) accelerates an object
of mass 1-kg at 1 m/s2.
Since F = ma, N = kg m/s2.
Forces
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Gravity
Tension
Compression
Contact
Friction
Electromagnetic
These forces, and ones
that are less familiar,
can be reduced to just
three fundamental ones.
The Fundamental Forces
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Gravity

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
~ 10-2 – 10-5
Tension, compression, contact, friction, electric, magnetic,…
Strong Force


Significant on large scales
Electroweak Force

~ 10-39
~1
Operates within protons and neutrons
For those who are interested in learning more about
that, go to http://www.particleadventure.org – you’ll
have a lot of fun! No formulas, just explanation of how
objects interact with each other
The Fundamental Forces
A basic question of current
physics is: do the fundamental
forces unify?
European Center for Particle Physics
http://www.cern.ch
The Force of Gravity
Mass and weight are different things.
Mass is a measure of inertia.
Weight is the force that gravity exerts on a body. It is not the
downward force of gravity, but the normal force exerted by the
surface one stands on, which opposes gravity and prevents one from
falling to the center of the Earth. This normal force is called the
apparent weight.
Example: A person with mass of 78 kg is riding in elevator which
is accelerating upward at 1.8 m/s2. What is the person’s
apparent weight?
W = m(a+g) = 78 (1.8+9.8) = 905 N
The Force of Gravity
Near the Earth’s surface, the weight of a stationary body
(body that does NOT move w.r.t ground), that is, the force
exerted on it by gravity is given by
w mg
where the magnitude of the vector g = 9.8 m/s2.
Example: A 1-kg object will have the same mass on the
Moon as on Earth, but will weigh less on the Moon than on
Earth. (Acceleration of gravity is only 1.6 m/s2 on the
Moon)
Clicker question 2
If I weigh 702 N on Earth and 5320 N on the surface if a
nearby planet, what is the acceleration due to gravity on
that planet?
1)
2)
3)
4)
5)
74.3 m/s2
54.2 m/s2
64.6 m/s2
85.5 m/s2
5.3 m/s2
Weightlessness
Aren’t astronauts “weightless”?
No. At typical space-shuttle
altitudes, the acceleration of
gravity is about 93% of its value
at Earth’s surface, so the
gravitational forces on the
shuttle and its occupants are
almost the same as on Earth.