Force and motion

A force is the effect that may produce a change in
the motion state, the size, or the shape of a body.
• A force is just a push or pull. Examples:
– an object’s weight
– tension in a rope
– friction
– attraction between an electron and proton
– Force is a vector!
• Bodies don’t have to be in contact to exert forces
on each other these are called Field Forces, e.g.,
gravity.

**Fundamental Forces of Nature
• Gravity
– Attraction between any two bodies (mass)
• Electromagnetic
– Forces between two bodies , attractive or repulsive
• Weak nuclear force – responsible for radioactive decay
• Strong nuclear force – holds quarks together (constituents of
protons and neutrons)

Note: information
starting with (**) are
for the advance
level.

**Galileo’s Thought Experiment

This
thought
experiment
lead to
Newton’s
First Law.

Newton’s First Law
“The Law of Inertia”

Objects at Rest

The downward force (mg) of gravity is balanced
by an upward force of the table (-mg).

A
c
c
e
l
e
r

a
t
i

o
n

Acceleration is the rate of change in velocity:
 A change in speed (magnitude)
 A change in direction
 A change in both magnitude (speed) and
direction

Newton’s First Law - Restated
• The velocity of an object remains
unchanged unless acted upon by a net
force.
or….
• An object will experience acceleration
if acted upon by a net force.

The Second Law of Motion

Units
m = mass = kilogram (kg)
a = acceleration = m/s2
Fnet = force = ma = kg∙m
s2
= Newton (N)
{Fnet} is sometimes written as { F}

nd
2

Law: Fnet = m a

• The acceleration of an object is directly
proportion to the net force acting on it (fig.1).
• For a given mass, if Fnet doubles, triples, etc., so
does a.
• The acceleration of an object is inversly
proportion to its mass(a = Fnet /m).
• For a given Fnet , if m doubles, a is cut in half.
• Fnet and a are vectors; m is a scalar.
• Fnet and a always point in the same direction.
• The 1st law is really a special case of the 2nd law (if
net force is zero, so is acceleration).

** Graph of Fnet vs. a
In the lab various known forces are applied—
one at a time, to the same mass—and the
corresponding accelerations are measured.
The data are plotted. Since Fnet and a are
directly proportional, the relationship is linear.
F

a

** Mass = Slope
Since slope (rise / run) = F / a, the slope is
equal to the mass.

so [m = F / a]
F
F

a
a

What is Net (Resultant) Force?
F1
F2
F3

Fnet

When more than one
force acts on a body,
the net force (resultant
force) is the vector
combination of all the
forces.
i.e. the resultant force
is the single force that
has the same effect as
all of the forces acting
on the object.

Resultant Force (cont.)
• When forces act in the same line, we can just add or subtract their
magnitudes to find the net force.

Resultant Force (cont.)
•When two perpendicular forces (F1 & F2)
act on an object, the magnitude of the net
force is: Fnet = ( F12 ) + ( F22 ) , and it’s
direction is between the two forces.
Examples of net forces:

Net Force & the 2nd Law
Example 1. Find the acceleration of the object in the figure.

32 N

15 N
2 kg

10 N

Fnet = 32 + 10 – 15 = 27 N to the right
a = Fnet /m = 27/2 = 13.5 m/s2, to the right.

Example 2. Find the acceleration of the object in the figure.
Fnet = ( F12 ) + ( F22 ) = ( 802 ) + ( 602 ) = 100 N
a = Fnet /m = 100/50 = 2 m/s2, direction shown in fig.

80 N

Fnet

50 Kg
60 N

Newton’s Third Law
"Every action
has an equal
and opposite
reaction"

The

RD
3

Law Restated
Forces always occur in
pairs. If object A
exerts a force F on
object B, then object
B exerts an equal and
opposite force –F on
object A.

Action – Reaction examples:
• If you hit a tennis ball with a racquet, the
force on the ball due to the racquet is the
same as the force on the racquet due to the
ball, except in the opposite direction.
• If you fire a rifle, the bullet pushes the rifle
backwards just as hard as the rifle pushes
the bullet forwards.
• If you drop an apple, the Earth pulls on the
apple just as hard as the apple pulls on the
Earth.

Earth / Apple
How could the forces on the tennis ball, apple, and
bullet, be the same as on the racquet, Earth, and rifle?
The 3rd Law says they must be, the effects are different
because of the 2nd Law!

e.g.

Apple’s weight = force
exerted by Earth on apple
= 3.92 N

Force exerted by apple
on Earth = 3.92 N
Earth

apple

Earth / Apple

a

(cont.)

F(from Earth on apple) = F(from apple on Earth)

m
Apple’s
little mass

=

Apple’s big
acceleration

m
Earth’s
big mass

in magnitude

a
Earth’s little
acceleration

Examples: 1. Lost in Space

Suppose an International Space Station
astronaut is on a spacewalk when her tether
snaps. Drifting away from the safety of the
station, what might she do to make it back?

2. Swimming
Due to the 3rd Law, when you swim you push the water
(blue), and it pushes you back just as hard (red) in the
forward direction. The water around your body also
produces a drag force-resistance- (green) on you, pushing
you in the backward direction. If the green and red cancel
out, you don’t accelerate (2nd Law) and maintain a constant
velocity.

Note: The blue vector is a force on the water, not the on
swimmer! Only the green and red vectors act on the swimmer.

3. The Slam Dunk
1. The player exerted a
downward force against
the earth (court)
2. The earth exerted a
reciprocal, upward force
upon the player
3. The force exerted by the
earth elevated the player
to the rim!

4. Demolition Derby
When two cars of
different size collide,
the forces on each are
the SAME (but in
opposite directions).
However, the same
force on a smaller car
means a bigger
acceleration!

Free fall
• An object is in free fall if the
only force acting on it is gravity.
• {air resistance is negligible }
Acceleration Due to Gravity
The acceleration due to
gravity, g, is constant for
objects near the Earth’s
surface :
g = 9.8 m/s2
Example: A Ball Drop

** Acceleration Sign Chart
Acceleration
Sign

(++)=+ (-+)=(+-)=- (--)=+

- 9.8 m/s2

Acceleration due to Gravity:
Near the surface of the Earth, all objects accelerate at the same
rate (ignoring air resistance) : { a = -g = -9.8 m/s2 }
This acceleration vector is the same if the object is thrown
upwards or downwards! because
, the object is
 (a) is (-). Also,
, the object is
 (a) is (-).

Galileo

Galileo dropped two cannon balls of different weights
from the top of Leaning Tower of Pisa. The two cannon
balls reached the ground at the same time. He proved
that when objects of different weights are dropped at
the same height and time, they take the same amount of
time to fall to the ground (ignoring air resistance).

** Speed against time graph for free falling
object

• In the absence of air resistance any body falling freely under
gravity falls with a constant acceleration.
• graph of speed against time is shown below

• The acceleration above is equal to the gradient of the graph
a = 9.8 m/s2 (this the magnitude of the free fall acceleration)

Mass and Weight
o Mass measures the amount of matter in an object,
it’s a scalar quantity.
o Weight is the force of gravity on a body, it’s a vector
quantity, it points toward the center of Earth.
o Weight = mass acceleration due to gravity
(this follows directly from F = m a).
•E.g. A body has a mass 120Kg,
what is its weight on earth?
•W = mg = 120 X 9.8 ≈ 120 x 10
= 1200 Newton

** Mass and Weight
(cont.)
On the moon, your
mass would be the
same, but your weight
would be less, this is
because the gravity of
the moon is less than
the gravity of Earth.
gmoon ≈ 1/6 gearth ≈ 1.6 m/s2
 W(on moon) ≈ 1/6 W(on earth)

Hippo & Ping Pong Ball
In vacuum, all bodies fall at the same rate.
If a hippo and a ping
pong ball were dropped
from a helicopter in a
vacuum (assuming the
copter could fly without
air), they’d land at the
same time.
When there’s no air resistance, size and shape don’t matter!

** Air Resistance ( drag force)
 It’s the friction force on an object
moving through air (or a fluid)
R
 Although we often ignore air
resistance ( R), it is usually significant
m in real life.
R
•
mg
•
•
•

depends on:
Speed (directly proportional to v2).
cross-sectional area
air density
other factors like shape

Terminal Velocity
Suppose a frog jumps out of a skyscraper window.
At first v = 0, so R = 0 too, and a = -g. As the frog
speeds up, R increases, and his acceleration
decreases. If he falls long enough his speed will be
big enough to make R = mg. When this happens
the net force is zero, so the acceleration must be
zero too.
R
This means the frog’s velocity can’t
change any more. He has reached his
terminal velocity. Small objects, like
raindrops and insects, reach terminal
velocity more quickly than large objects.

mg

The speed against time graph
for a falling parachutist
•

In reality gravity is not the only force acting on any body falling
through air, there is also air resistance.
1000 N

1000 N

(1) The parachutist jumps from the aircraft with his parachute closed.
(2) Speed increases, air resistance increases, the acceleration decreases.
(3)&(4) Steady (terminal) speed, air resistance = weight, net force = 0, acceleration = 0.
(5) The parachutist opens his parachute. The air resistance increases suddenly, the

parachutist starts to decelerate rapidly, speed decreases.
(6) The parachutist still slowing down .
(7) & (8) The parachutist reaches terminal speed, which is less than the speed in (3).

Forces & Motion
To solve motion problems involving forces:

1. Find
2. Calculate
3. Use

(by combining vectors).
(using: Fnet = m a).

a=(v2-v1)/t or
v2= v1+ a t
d = v1×t + 1 a t2
2
V22 = v12 + 2 a d
d = ½ (v2+v1) × t

Samples Problem
Samira 400 N
Fadi 1200 N

Treasure 300 kg
Samia 850 N

1. Tow girls are fighting with a boy over a treasure
box, initially at rest. Find:
a. Fnet
b. a

= 50 N left

=1/6=0.167 m/s2 left

c. (v) after 5 s

=5/6=0.835 m/s left

d. (d) after 5 s

=25/12=2.08 m left

Sample Problems (cont.)
2. You’re riding a unicorn at 16 m/s and come to a uniform
stop at a red light 20 m away. What’s your acceleration?
3. A brick is dropped from 80 m up. Find its impact velocity
and air time.
4. An arrow is shot straight up from a pit 12 m below ground
at 18 m/s.
a. Find its max height above ground.
b. At what times is it at ground level?
5. A catcher catches a 36 Kmph fast ball. His Remember the converging
glove compresses 5 cm. How long does it rules:
(m/s) x (3.6)  Km/h
take to come to a complete stop?
(Km/h) ÷ (3.6)  (m/s)
Answers: Q2. a = -6.4 m/s2.
Q3. v = 40 m/s, t = 4 s.
Q4. (a) d = 16.2 m, (b) t = 3.6 s.
Q5. t = 0.01 s.

(cm) ÷ 100  (m)
(m) X 100  (cm)

** Multi-step Problems
1. How fast should you throw a kumquat
straight down from 40 m up so that its
impact speed would be the same as a
mango’s dropped from 60 m?
Answer: 19.8 m/s

2. A dune buggy accelerates uniformly at
1.5 m/s2 from rest to 22 m/s. Then the
brakes are applied and it stops 2.5 s later.
Find the total distance traveled.
Answer: 188.83 m

Fun Freefall Problems!!!!
1) A ‘coin’ is dropped from the top of a rollercoaster.
The height of the ride is 110m.
Neglecting air resistance, Find:
a. The speed of the coin when it hits the ground.
b. The time it takes for the coin to fall to the ground.
c. Would it be different for a heavier coin?
Answers: (a) 44.7 m/s.

(b) 4.47 s.

(c) No, because the free fall acceleration is constant
for all objects as long as air resistance is negligible.

2) A stone is thrown straight upward with a
speed of 20 m/s.
a) How high does it go?
b) How long does it take to rise to its
maximum height?
3) An object is thrown straight upward
and falls back to the thrower after a
time of 0.80 s.
How fast was the object thrown?
Answers:
2. (a) d = 20 m.
3. v1 = 4 m/s

(b) t = 2 s.

4)A cell phone is thrown
downward from the edge of
a building with a velocity of
20 m/s and it reached the
ground after 4 seconds.
a. Calculate the height of the
building.
b. Where will the object be
after 2 seconds?
Answers:
(a) 160 m .
(b) 80 m above earth, on its way
down.

5) Bobo throws an apple vertically
upward from a height of 1.3 m with
an initial velocity of 8 m/s.
a) Will the apple reach a friend in a tree
3.5 metres above the ground?
a) If the apple is not caught, how long
will the apple be in the air before it

hits the ground?

Misconceptions
• If an object is moving, there must be a net force making it move.
• Wrong! It could be moving without accelerating.
• Heavy objects must fall faster than light ones.
• Wrong! The rate is the same in vacuum, or when air resistance is
negligible (i.e. veryyyyyy small compared to object’s weight).
• When a big object collides with a little one, the big one hits the little
one harder than the little one hits the big one.
• Wrong! The 3rd Law says they hit it each other with the same force,
but the little object will gain a greater acceleration.
• If an object accelerates, its “speed” must change.

• Wrong! It could be turning at constant speed (i.e. direction changes
but not magnitude, so “velocity” is changing) .

** Normal force
• When an object lies on a table or on the
ground, the table or ground must exert an
upward force on it, otherwise gravity would
accelerate it down.
• This force is called the normal force, and it’s a
“contact force” not a “field force” (i.e. it
wouldn’t occur unless there is contact between
the object and the surface.
N
In this particular case,
m
N = mg (N. 3rd law).
So, Fnet = 0; objects at rest
stays at rest, unless ……
mg
( N. 1st law).

** Normal forces aren’t always vertical
―Normal‖ means perpendicular. A normal force
is always perpendicular to the contact surface.
N

mg

For example, if a
flower pot is setting
on an incline, N is
not vertical; it’s at a
right angle to the
incline.

Friction
Friction is the force that bodies can exert on each other
when they’re in contact.
The friction forces are parallel to the contact surface
and opposite to the direction of motion.

v
Fr

object

surface

Friction Facts
• Friction is due to electrostatic attraction
between the atoms of the objects in contact.
• It allows you to walk, turn a corner on your
bike, and warm your hands in the winter.
• Friction often causes energy waste .
• It makes you push harder and longer to attain
a given acceleration.

Friction Example
You push a giant barrel on a surface with a
constant force (F) of 63 N to the left. If the
barrel moved with constant velocity, what is
the friction force (Fr )?
Barrel

Answer: v=constant  a=0  Fnet = 0  Fr=F in
magnitude and opposite in direction (balanced
forces)  Fr = 63 N to the right.

Suppose you drive a car in a circle at a constant speed.
Even though your speed isn’t changing, you are accelerating.
This is because acceleration is the rate of change of velocity(not speed),
and your velocity is changing because your direction is changing.
This acceleration is called centripetal acceleration.

Circular motion is due to forces acting perpendicular
to the direction of motion,

such forces are called centripetal forces

The force that changes the straight path of
a particle into a circular or curved path is
called the: ‘centripetal force’
It is a pull on the body and is directed
toward the center of the circle.

Without a centripetal
force, an object in
motion continues
along a straight-line.

With a centripetal force,
an object in motion will
be accelerated and
change its direction.

Remember
Newton’s 1st Law?

What is the
centripetal force?

Centripetal forces

1. Friction, as in the turning car example
2. Tension, as in a rock whirling around while
attached to a string,
or the tension in the chains on a swing at the
park.
Gravity: The force of gravity between the Earth
and sun keeps the Earth moving in a nearly
circular orbit.

Force and motion

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