Chapter 5
Chapter 5
Force and Motion I
5 Force and Motion I
March 14, 2022 2PHY101 Physics I © Dr.Cem Özdoğan
March 14, 2022 3PHY101 Physics I © Dr.Cem Özdoğan
5-2 Newtonian Mechanics
Mechanics of Particle Motion
1. Newtonian Mechanics: Study of relation between force and
acceleration of a body.
•
Sir Isaac Newton (1642-1727)
•
Three laws relating force and motion.
•
Valid for a wide range of speed and scale of
interacting bodies. Valid for our daily life.
•
Newtonian Mechanics does not hold good for all situations!
2. Special Theory of Relativity
•
Albert Einstein (1879-1955)
•
Holds for all speed including close to speed of light.
•
Replaces Newtonian Mechanics for very large speed.
3. Quantum Mechanics
•
Replaces Newtonian Mechanics for interacting bodies on the
scale of atomic structure (very small).
•
A force is a “push”or “pull” acting on a object and causes acceleration.
F ~ a
March 14, 2022 4PHY101 Physics I © Dr.Cem Özdoğan
5-3 Newton’s First Law
•
A body at rest tends to remain at rest & a body in motion at a constant
velocity will tend to maintain the velocity.
If no force acts on a body, the body’s velocity cannot change; that
is, the body cannot accelerate.
Before Newtonian mechanics; Some influence (force) was thought necessary
to keep a body moving. The “natural state” of objects was at rest.
March 14, 2022 5PHY101 Physics I © Dr.Cem Özdoğan
5-4 Force
•
A force is measured by the acceleration it produces.
–
Forces have both magnitudes and directions.
•
Principle of superposition of forces:
•
A net force has the same impact as a single force with identical
magnitude and direction.
net
F
: Sum of forces acting on a body (net force, resultant force)
1 Newton = 1 kg.m/s² (SI)
March 14, 2022 6PHY101 Physics I © Dr.Cem Özdoğan
5-5 Mass
•
What is mass?
•
Mass is the property of an object that measures how hard it is to change
its motion. Body’s resistance to a change in velocity.
–
It is an intrinsic characteristic of a body. It is not the same as
weight, density, size etc.
–
The mass of a body is the characteristic that relates a force on the
body to the resulting acceleration (F~a → F=ma).
•
The ratio of the masses of two bodies is equal to
the inverse of the ratio of their accelerations when
the same force is applied to both.
Example Apply an 8.0 N force to various bodies:
Mass: 1kg → acceleration: 8 m/s
2
Mass: 2kg → acceleration: 4 m/s
2
Mass: 0.5kg → acceleration: 16 m/s
2
Acceleration: 2 m/s
2
→ mass: 4 kg
March 14, 2022 7PHY101 Physics I © Dr.Cem Özdoğan
5-6 Newton’s Second Law
Identify the body in question, and only include forces that act on that
body! Separate the problem axes (they are independent):
March 14, 2022 8PHY101 Physics I © Dr.Cem Özdoğan
5-6 Newton’s Second Law; Drawing a free-body diagram (FBD)
•
In a free-body diagram, the only body shown
is the one for which we are summing forces.
–
Each force on the body is drawn as a
vector arrow with its tail on the body.
–
A coordinate system is usually included.
–
Acceleration is NEVER part of a free
body diagram - only forces on a body are
present.
If the net force on a body is zero:
•
Its acceleration is zero
•
The forces and the body are in equilibrium
•
But there may still be forces!
statics
COM
March 14, 2022 9PHY101 Physics I © Dr.Cem Özdoğan
Example:
Fig. 5-3 In three situations, forces act on a
puck that moves along an x axis.
5-6 Newton’s Second Law
March 14, 2022 10PHY101 Physics I © Dr.Cem Özdoğan
Example:
5-6 Newton’s Second Law
March 14, 2022 11PHY101 Physics I © Dr.Cem Özdoğan
5-7 Some Particular Forces
1) The Gravitational Force:
A gravitational force on a body is a certain type of pull that is directed
toward a second body.
2) Weight:
The weight, W, of a body is equal to the magnitude F
g
of the gravitational
force on the body.
W = mg (weight),
or
CAUTION: A body’s weight is not its mass!
EARTH!
-F
g
= m(-g) or F
g
= mg.
March 14, 2022 12PHY101 Physics I © Dr.Cem Özdoğan
3) Normal Force: (Normal means perpendicular)
For any vertical acceleration a
y
of the table and block.
When a body presses against a surface, the
surface (even a seemingly rigid one)
deforms and pushes on the body with a
normal force, F
N
, that is perpendicular to
the surface.
Fig. 5-7 (a) A block resting on a table experiences
a normal force perpendicular to the tabletop. (b)
The free-body diagram for the block.
In the figure: Newton’s second law says
for a positive-upward y axis:
(F
net, y
=
ma
y
), as:
5-7 Some Particular Forces
March 14, 2022 13PHY101 Physics I © Dr.Cem Özdoğan
4) Friction:
•
If we either slide or attempt to slide a body over a
surface, the motion is resisted by a bonding between the
body and the surface.
•
The force f is either called frictional force or simply
friction. Directed along the surface, opposite to the
direction of intended motion.
•
Sometimes, to simplify a stiuation, friction is assumed to be negligible.
(So the surface is frictionless.)
5) Tension
Fig. 5-9 (a) The cord, pulled taut, is under tension. If its mass is negligible,
the cord pulls on the body and the hand with force T, even if the cord runs
around a massless, frictionless pulley as in (b) and (c).
•
When a cord is attached to a
body and pulled taut, the
cord pulls on the body with a
force T directed away from
the body and along the cord.
5-7 Some Particular Forces
motion no motion yet
March 14, 2022 14PHY101 Physics I © Dr.Cem Özdoğan
5-8 Newton’s Third Law: Symmetry in Forces
•
When two bodies interact, the forces on the bodies from each other are
always equal in magnitude and opposite in direction and collinear.
•
The forces between two interacting bodies are
called a third-law force pair.
same
direction!?
|F
BC
|=|F
CB
|
|F
PW
|=|F
WP
|
March 14, 2022 15PHY101 Physics I © Dr.Cem Özdoğan
5-8 Newton’s Third Law
2) Compare the magnitudes of the acceleration you experience, a
A
, to the magnitude of
the acceleration of the spacecraft, a
S
, while you are pushing:
1. a
A
= a
S
2. a
A
> a
S
3. a
A
< a
S
1) Suppose you are an astronaut in outer space giving a brief push to a
spacecraft whose mass is bigger than your own. Compare the magnitude of the
force you exert on the spacecraft, F
S
, to the magnitude of the force exerted by
the spacecraft on you, F
A
, while you are pushing:
1. F
A
= F
S
2. F
A
> F
S
3. F
A
< F
S
correct
correct
a=F/m
(F same lower mass gives larger a)
Third
Law!
March 14, 2022 16PHY101 Physics I © Dr.Cem Özdoğan
5-9 Applying Newton’s Laws
Do we have a
MOTION?
First step → FBDs: draw for all masses & directions
Second step → decide coordinate systems
y:
x:
M
M
m
M
m
F
gH
-T=+ma
xm
Same with previous one as multiplied by minus sign
10/20/26 17PHY101 Physics I © Dr.Cem Özdoğan
5-9 Applying Newton’s Laws
March 14, 2022 18PHY101 Physics I © Dr.Cem Özdoğan
Example : Cord accelerates block up a ramp
Using Newton’s Second
Law, we have :
which gives:
The positive result indicates
that the box accelerates
up the plane.
5-9 Applying Newton’s Laws
θ
θ
March 14, 2022 19PHY101 Physics I © Dr.Cem Özdoğan
Example : Reading a force graph
Answer: a
x
=-2 m/s
2
5-9 Applying Newton’s Laws
March 14, 2022 20PHY101 Physics I © Dr.Cem Özdoğan
Example: Forces within an elevator cab
•
The reading is equal to the magnitude of
the normal force on the passenger from the
scale.
•
We can use Newton’s Second Law only in
an inertial frame. If the cab accelerates,
then it is not an inertial frame. So we
choose the ground to be our inertial frame
and make any measure of the passenger’s
acceleration relative to it.
5-9 Applying Newton’s Laws
March 14, 2022 21PHY101 Physics I © Dr.Cem Özdoğan
Example (Continued): Forces within an elevator cab
5-9 Applying Newton’s Laws
March 14, 2022 22PHY101 Physics I © Dr.Cem Özdoğan
Example: Acceleration of block pushing on block
Answer: a
x
=2 m/s
2
,
F
BA
=12 N
5-9 Applying Newton’s Laws
March 14, 2022 23PHY101 Physics I © Dr.Cem Özdoğan
Example:
(OpenStax 4.6) Calculate the tension in the wire supporting the 70.0-kg
tightrope walker shown in Figure.
March 14, 2022 24PHY101 Physics I © Dr.Cem Özdoğan
(Serway 5.4) A traffic light weighing 122 N hangs from a cable tied to two
other cables fastened to a support as in Figure. The upper cables make angles of
37.0° and 53.0° with the horizontal. These upper cables are not as strong as the
vertical cable and will break if the tension in them exceeds 100 N. Does the
traffic light remain hanging in this situation, or will one of the cables break?
Example:
2 unknowns (T
1
, T
2
) & 2 equations
Both < 100 N √
=ma
x
=ma
y
March 14, 2022 25PHY101 Physics I © Dr.Cem Özdoğan
(Serway 5.9) When two objects of unequal mass are hung vertically over a
frictionless pulley of negligible mass as in Figure, the arrangement is called an
Atwood machine. The device is sometimes used in the laboratory to calculate
the value of g. Determine the magnitude of the acceleration of the two objects
and the tension in the lightweight cord.
Example:
ignore the weight of the cord
System
acceleration
a
ym1
=a
ym2
=a
??
check if
m
2
>m
1
or
m
2
<m
1
eliminate T
-1*(T-m
2
g)=-m
2
a
y
Same!
March 14, 2022 26PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
1. In Figure, let the mass of the block be 8.5Zkg and the
angle be 30°. Find (a) the tension in the cord and (b) the
normal force acting on the block. (c) If the cord is cut,
find the magnitude of the resulting acceleration of the
block.
1
a
x
: not zero any more
March 14, 2022 27PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
2. A car traveling at 53Zkm/h hits a bridge abutment. A passenger in the car moves
forward a distance of 65Zcm (with respect to the road) while being brought to rest
by an inflated air bag. What magnitude of force (assumed constant) acts on the
passenger's upper torso, which has a mass of 41Zkg?
constant acceleration
March 14, 2022 28PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
3.A car that weighs 1.30x10
4
N is initially moving at 40Zkm/h when the brakes are
applied and the car is brought to a stop in 15Zm. Assuming the force that stops the car
is constant, find (a) the magnitude of that force and (b) the time required for the
change in speed. If the initial speed is doubled, and the car experiences the same
force during the braking, by what factors are (c) the stopping distance and (d) the
stopping time multiplied?
March 14, 2022 29PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
3. (Continued) A car that weighs 1.30x10
4
N is initially moving at 40Zkm/h when the
brakes are applied and the car is brought to a stop in 15Zm. Assuming the force that
stops the car is constant, find (a) the magnitude of that force and (b) the time required
for the change in speed. If the initial speed is doubled, and the car experiences the
same force during the braking, by what factors are (c) the stopping distance and (d)
the stopping time multiplied?.
March 14, 2022 30PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
4. An elevator cab and its load have a combined mass of 1600Zkg. Find the tension in
the supporting cable when the cab, originally moving downward at 12Zm/s, is
brought to rest with constant acceleration in a distance of 42Zm.
v
0
v
f
=0
Δx
=y
f
-y
i
y
f
y
i
March 14, 2022 31PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
5. Figure shows a box (mass m
1
=3.0 kg) on a
frictionless plane inclined at angle θ
1
=30
o
. The
box is connected via a cord of negligible mass to
a box (mass m
2
=2.0 kg) on a frictionless plane
inclined at angle θ
2
=60
o
. The pulley is
frictionless and has negligible mass. What is the
tension in the cord?
March 14, 2022 32PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
Solved Problem 5
March 14, 2022 33PHY101 Physics I © Dr.Cem Özdoğan
5 Solved Problems
5. (Continued) Figure shows a box (mass m
1
=3.0
kg) on a frictionless plane inclined at angle θ
1
=30
o
. The box is connected via a cord of
negligible mass to a box (mass m
2
=2.0 kg) on a
frictionless plane inclined at angle θ
2
=60
o
. The
pulley is frictionless and has negligible mass.
What is the tension in the cord?
March 14, 2022 34PHY101 Physics I © Dr.Cem Özdoğan
5 Summary
Newtonian Mechanics
Forces are pushes or pulls
Forces cause acceleration
Force
Vector quantities
1 N = 1 kg m/s
2
Net force is the sum of all
forces on a body
Inertial Reference Frames
Frames in which Newtonian
mechanics holds
Newton's First Law
If there is no net force on a
body, the body remains at
rest if it is initially at rest, or
moves in a straight line at
constant speed if it is in
motion.
March 14, 2022 35PHY101 Physics I © Dr.Cem Özdoğan
5 Summary
Mass
The characteristic that
relates the body's
acceleration to the net force
Scalar quantity
Newton's Second Law
Free-body diagram
represents the forces on one
object
Newton's Third Law
Law of force-pairs
If there is a force by B on C,
then there is a force by C
on B:
Some Particular Forces
Weight:
Normal force from a surface
Friction along a surface
Tension in a cord
Eq. (5-1)
Eq. (5-12)
Eq. (5-15)
March 14, 2022 36PHY101 Physics I © Dr.Cem Özdoğan
Additional Materials
5 Force and Motion I
March 14, 2022 37PHY101 Physics I © Dr.Cem Özdoğan
5-4 Force; Inertial Reference Frames
(a) The path of a puck sliding from
the north pole as seen from a
stationary point in space. Earth
rotates to the east. (b) The path of
the puck as seen from the ground.
•
If a puck is sent sliding along a short strip of frictionless ice—the puck’s
motion obeys Newton’s laws as observed from the Earth’s surface.
•
If the puck is sent sliding along a long ice strip extending from the north
pole, and if it is viewed from a point on the Earth’s surface, the puck’s path
is not a simple straight line.
•
The apparent deflection is not caused by a force, but by the fact that we see
the puck from a rotating frame. In this situation, the ground is a
noninertial frame.
March 14, 2022 38PHY101 Physics I © Dr.Cem Özdoğan
Force; The Four Basics Forces
