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ACCELERATED PHYSICS
CHAPTER 4:
FORCES & NEWTON’S LAWS OF MOTION
Name: ______________________________
Period: ______________________________
Teacher: ______________________________
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MASS
 The “amount” of matter, or “stuff” that makes up an object.
 The amount of inertia an object has.
INERTIA
Definition: an objects tendency to resist a change in its present state of motion.
 Inertia is related to the amount of mass an object has
Ex: An 8 kg object has twice the inertia of a 4 kg object.
“Resisting a change in motion”
 If an object is at rest, the objects inertia is a measure of how much it wants to
remain at rest
 If an object is moving with a constant velocity, the objects inertia is a measure of
how much it wants to remain moving at a constant velocity (maintaining speed as
well as direction of travel)
FORCE
Definition: A push or pull on an object – it is the “thing” that causes objects to
accelerate. By pushing or pulling an object you are applying a force to the object.
 Force are measured in units of Newtons (N)
o 1 “Newton” is the amount of force needed to accelerate a 1 kg mass at 1
m/s2
 It’s hard to talk about acceleration without stating the “thing” that caused the
acceleration to begin with.
For example:
The acceleration due to gravity
The deceleration of a car due to friction
 Forces cannot be seen, they are only known by the effects they cause
(accelerations).
 An object needs to be present in order for a force to act on it!
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Newton’s Three Laws of Motion
1st Law: The Law of Inertia – “an object at rest will stay at rest, an object in motion will
stay in motion, unless acted upon by a net force”
Net Force – the combination of all the forces acting on one object. The net force is the
magnitude of the force left over after you add or subtract all the forces acting on an
object.
 The Greek capital letter sigma “Σ” means “the sum of”. ΣF is what we use to
denote “the sum of the forces” on an object, or the net force.
 If the net force (ΣF) on an object equals zero, then the acceleration of the object is
equal to zero!
Does this mean that if the net force is zero (ΣF = 0) there are no forces acting on the
object?
⃑ =
2nd Law: (𝒂
∑ ⃑𝑭
𝒎
) The acceleration of an object is directly proportional to the net force
on it, and inversely proportional to its mass. The direction of the acceleration vector will
be in the direction of the net force vector.
Newton’s Second Law is commonly rewritten as ∑ 𝐹 = 𝑚𝑎
Example: A force of 100 Newtons is applied to a 5 kg object. What’s the acceleration of
the object?
Example: What force is needed to acceleration a 20 kg object at 10 m/s2?
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3rd Law: Action/Reaction Forces – When one object exerts a force on a second object,
the second object will exert a force on the first object. The second force is equal in
magnitude and opposite in direction to the first force.
Written as a formula:
This is more commonly known as “every action has an equal and opposite reaction”.
Newton’s third law states that forces always come in pairs
Force on Tray
by Hand
Using the picture to the right….
 Action: the force on the tray by the hand
 Reaction: the force on the hand by the tray
Force on Hand
by Tray
EARTH
What about an object resting on a table on the surface of the Earth?
 Force exerted on the block by the earth, and force on the Earth by the block
 Force exerted on the table by the block, and force on the block by the table
 Force exerted on the Earth by the table, and force on the table by the Earth
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An object is falling towards the surface of the earth
 An object in free fall has a gravitational force on the object by the earth.
 According to Newton’s 3rd Law, an identical (but opposite) gravitational force is
exerted on the earth by the falling object.
 If this is true, this means that the earth experiences an acceleration.
Ball in free fall
g
Force
of gravity
a
Reaction to the
Force of gravity
EARTH
A slightly different scenario: 2 rocks are falling towards the surface of the earth. Rock A
has a mass of 2 kg. Rock B has a mass of 4 kg. How do the accelerations of each rock
and the forces on each rock compare to one another? (NOTE: here we’re only talking
about the two rocks, we’re NOT looking at the force or acceleration on the earth)
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Lesson 1 Conceptual Questions and Problems
1. Why does a child in a wagon seem to fall backward when you give the wagon a
sharp pull?
2. Only one force acts on an object. Can the object have zero acceleration? Can it
have zero velocity?
3. The force of gravity on a 20 kg rock is twice as great as that on a 10 kg rock.
When then doesn’t the heavier rock fall faster?
4. You’re leaning on a wall with 40 Newtons of force. Using Newtons 3rd Law
describe the “reaction” force by stating (A) its magnitude, (B) its direction, (C) on
what object it is exerted, and (D) by what body it is exerted.
5. A net force of 125 N is applied to a certain object. As a result, the object
accelerates at 24 m/s2. What’s the mass of the object?
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6. A catcher stops a 0.1 kg ball travelling at 40 m/s in a distance of 0.2 m. What is
the force exerted on the ball? What’s the force exerted on the catcher’s glove?
7. What is the net force required to accelerate a 1200 kg car from rest to 27 m/s in
10 seconds?
8. A car starting from rest travels 150 meters in 8 seconds. What’s the force on a 65
kg passenger in the car?
9. Two dogs are playing tug-of-war with a toy. If dog A (Rufus) is pulling to the right
with 15 N, and dog B (Harold) is pulling to the left with 10 N, what’s the
acceleration of the 1.5 kg toy?
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Common Forces
1. Weight (Fg) – The force due to Gravity
𝐹𝑔 = 𝑚𝑔
Where:
m (mass) is measured in kilograms (kg)
g (acceleration due to gravity) is measured in m/s2
g = -9.8 m/s2
 An object experiences this force when they’re in a gravitational field of another
object (typically another planet or star like Earth or the Sun)
 Weight and Mass are two different quantities… they are NOT synonyms!
 The force due to gravity always points straight down even when on a ramp!
2. The Normal Force (FN) – The force from being in contact with another object
 An object experiences this force when resting against something else, such as a table,
wall, or even another object.
 Normal Force is reactive not proactive, meaning it doesn’t exist unless we’re actually
resting against something else.
 Normal Force is always perpendicular to the surface, even if the object is on a ramp.
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3. Tension (FT) – The force from a string, rope, or cable.
 Tension forces pull, never push
 Tension forces always act along the string
 Tension force is a reactive force, meaning something must pull on the rope to have
tension in the rope.
4. Friction (Ffr) – Surface force resisting the motion of an object, parallel & opposite
the direction of motion.
𝐹𝑓𝑟 = 𝜇𝐹𝑁
Where:
µ (Greek letter “mu”) is the coefficient of friction. This unit-less.
FN is the Normal Force on the object
 Friction is only present when normal force is present (when we’re against a surface)
Static Friction vs Kinetic Friction (µs vs µk)
 µ is a number specific for the two surfaces in contact
 “Static” friction (µs) meaning “not moving”
o This is the resistance you feel when trying to get an object to start sliding
 “Kinetic” friction (µk) meaning “moving”
o This is the resistance you feel when sliding an object on the floor
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Free Body Diagrams
A free body diagram is a way to show all the forces acting on an object. The object is
represented as a dot, and all the forces acting on that object are drawn leaving the dot.
Draw the free body diagram for the situations described below:
A book is at rest on a table top
A box is suspended from a string attached
to the ceiling
A sled is being pulled with a horizontal
rope while on ice (assume frictionless)
A sled is being pulled with a horizontal
rope while on pavement (assume friction)
A car is coasting to the right and slowing
down
Playing tug of war over a chew toy with
your dog. Dog pulls horizontally, you pull
45° above the horizontal
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Steps for Solving Force Problems:
1. Draw a free body diagram for all the forces acting on an object. If there is more than
one object you’ll need more than one free body diagram.
a. Are we in a gravitational field? If yes, then we have gravity. (Pointing down)
b. Are there any strings, ropes, or cables? If yes, then we have tension. (pointing
along the rope)
c. Is there friction? If yes, then friction points opposite the direction of motion,
parallel to the surface.
d. Are we resting on a surface such as a table? If yes, we have normal force
(pointing perpendicular to the surface-surface contact)
2. Start with Newton’s Second Law (ΣF = ma)
a. If you have at least one force pointing in the x-direction you’ll need to use
Newton’s Second Law for the x-direction.
b. If you have at least one force pointing in the y-direction you’ll need to use
Newton’s Second Law for the y-direction.
c. If you have at least one force pointing at an angle (meaning it has x & y
components) you’ll need to use Newton’s Second Law for the x & y directions.
3. Is the object accelerating in the x or y direction? If not, ax and ay in Newton’s Second
Law are equal to zero.
4. Sum the forces for the x or y direction. Forces pointing along the positive x or y
directions are considered positive. Forces pointing along the negative x or y
directions are considered negative. (same for x & y components of forces pointing at
angles)
5. Make substitutions with known values, change Fg to mg, or Ffr to µFN.
6. Simplify and solve.
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Example: Tension Problem
One paint bucket weighing 35 N is hanging from a massless cord from another bucket
weighing 40 N. The two are being pulled upward with an acceleration of 1.5 m/s2 by a
massless cord attached to the top bucket. Calculate the tension in each cord.
a = 1.5 m/s2
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Example: Friction Problems
1. A 35 kg crate is resting on a floor.
a. Find the force needed to drag the crate on a frictionless floor with a rope at
a constant speed.
b. Find the force needed to drag the crate on a floor where the coefficient of
friction is 0.30.
2. A box on a table is being pulled horizontally with a force of 80 N. The mass of the
box is 35 kg and there is a frictional force of 15 N opposing the box’s motion. Find
the normal force on the box and the horizontal acceleration of the box
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Example: Angled Force Problem
A box is being pulled by a rope with a tension of 60 N at an angle of 55 degrees to the
horizontal. The coefficient of friction between the box and the surface is 0.25. If the
box has a mass of 15 kg, find the horizontal acceleration.
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Common Forces Problems
1. How much tension must a rope withstand if it is used to accelerate a 1050 kg car
horizontally at 1.20 m/s2? Ignore friction.
2. Find the tension needed to pull a 1300 kg elevator upward at a constant velocity
3. If the coefficient of kinetic friction between a 35 kg crate and the floor is 0.30,
what horizontal force is required to move the crate at a steady speed across the
floor? What horizontal force is required if the floor is frictionless?
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4. A 50 kg crate is being pulled along a horizontal smooth surface. The pulling force
is 10.0 N and is directed 20 degrees above the horizontal. What is the magnitude
of the acceleration of the crate?
5. A horizontal force of 35 N is applied to an object by pulling a rope. If the surface
the box is on has a coefficient of kinetic friction of 0.15 and the box has a mass of
7 kg, find (A) the normal force, (B) the weight, (C) frictional force, and (D) the
acceleration of the box.