POPS Unit 2 Teacher Notes – Forces 2013
Systems and Dynamics
Force - Any influence that causes an object to change in its motion or direction.
Systems
-All the objects involved in the problem
-Usually only two objects
Two objects hit, and then one of those objects hits another.
Dynamics - The study of the effects of forces on matter in a system
Internal Versus External Forces
Internal forces
Forces which originate within the system.
Objects exert the forces on each other
Cannot change the total momentum of a system
Example: the objects pushing against each other
External forces
Forces which originate outside the system.
Can change the total momentum of a system
Example: gravity pulling the objects down (unless gravity is part of the system)
Fundamental Forces
Four Fundamental Forces of the Universe
Gravitational
Electromagnetic
Strong Nuclear
Weak Nuclear
Gravitational
Definition: Force of attraction between masses
Weakest of the 4 types
Long range
One of the most observable forces
Electromagnetic
Definition: Forces between charged particles
Much stronger than gravitation
Shorter (but still long) range.
One of the most observable
Strong Nuclear
Definition: Force that holds the nucleus of an atom together
Strongest force, overcoming strong repulsive forces in the nucleus,
Short range
Not easily observable
Weak Nuclear
Definition: Force that holds individual protons and neutrons together.
Involved in radioactive β decay
One of the strongest forces
Very short range
Very difficult to observe
(quarks)
Newton’s Laws
Who was Isaac Newton?
1642 - 1727
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One of the greatest scientists of all time
In 1665, wrote Philosophiae Naturalis Principia Mathematica
Mathematical Principles of Natural Philosophy
Constructed three laws of motion:
The Law of Inertia
The Law of Unbalanced Force
The Law of Action and Reaction
Newton’s 1st Law
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The Law of Inertia - The Tendency to Resist Change in Motion
An object at rest stays at rest, and object in motion stays in motion unless acted on by an outside, unbalanced
force.
Objects keep on doing what they’re doing.
Example:
Fill up a baking dish with water. It would spill under the following circumstances:
the container was at rest and you attempted to move it
The container was in motion and you attempted to stop it
The container was moving in one direction and you attempted to change its direction
Newton’s 2nd Law
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When an unbalanced force acts on an object, the object will be accelerated.
Acceleration varies directly with the unbalanced force and in the same direction as the applied force.
Written Mathematically says
𝐹
a=
𝑚
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This is commonly written as
F=
m
a
N=
kg
m/s2
Force is measured in Newton’s (N).
Force is a vector quantity.
Applications of Newton’s 2nd Law
Newton’s 3rd Law
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The Law of Action and Reaction
Every force is accompanied by an equal but opposite force.
Forces always come in pairs – equal and opposite action reaction pairs
Example
A bird stays in the air by flapping its wings down.
The motion of the wings is down
The acceleration is up.
The opposite reaction force of the air against the wings is what causes the motion.
Free Body Diagrams
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Diagrams used to show the relative magnitude and direction of all forces acting upon an object in given
situation.
All forces in a system must be drawn.
No limit on total number of forces.
Forces are shown with an arrow pointing away from the system.
Length of the arrow is relative to the force.
Types of forces
Normal Force -Force normal is equal to the force of the weight of the object
𝐹𝑛 = 𝐹𝑤
Applied Force - A force applied to an object. It may be balanced or unbalanced by other forces.
Friction Force -The resistance to motion between 2 objects in contact
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Kinetic friction
The friction between objects moving with respect to one another.
Static friction
Friction between objects that are not moving with respect to one another.
Static friction is greater than kinetic friction
Friction is an electromagnetic force
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Coefficient of Friction (µ)
Describes the nature of the surfaces in contact
Does not describe the nature of the objects
𝐹𝑓 = µ𝐹𝑛
Air Resistance
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The frictional force between air molecules and the surface of a falling object.
Terminal Velocity
𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝐹𝑤𝑒𝑖𝑔ℎ𝑡
When the upward force due to air resistance equals the weight of the object:
Acceleration stops
Velocity becomes constant
Two primary factors affect terminal velocity
Area of the object
How much air is caught underneath the object
Mass of the object
How much air can be pushed out of the way
Terminal Velocity
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How would a large surface area affect an object’s terminal velocity?
How would a large mass affect an object’s terminal velocity?
Mass versus Weight
Mass
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Depends on the amount of matter in an object
Stays the same – does not change due to gravity
May change if something is taken away or added to it.
Scalar
Weight
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Weight refers to gravitational force exerted on the object
Changes in weight depend on location.
The farther out from earth, the less you weigh.
Vector
To find the weight of a mass…
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Use Newton’s 2nd Law
𝐹𝑤 = ma
w = weight
m = mass
g = acceleration due to gravity
𝐹𝑤 = mg
Momentum and Impulse
Momentum
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All objects in motion have momentum
𝑝 = 𝑚𝑣
𝑘𝑔∙𝑚
Unit is 𝑠
Vector quantity
direction is the same direction as the velocity
Conservation of Momentum
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When 2 bodies collide, the total momentum before the collision is equal to the total momentum after the
collision.
𝑝𝑖 = 𝑝𝑓
This is another way of wording Newton’s 3rd Law:
The Law of Action and Reaction
Every force is accompanied by an equal but opposite force.
A gain of momentum by one object results in an equivalent loss of momentum by the other object
𝑝𝑖𝑎 + 𝑝𝑖𝑏 = 𝑝𝑓𝑎 + 𝑝𝑓𝑏
Momentum is conserved regardless of the direction of movement after the collision
Impulse
 The product of an unbalanced force and the time interval over which it is exerted is called impulse
∆p=m∆v
∆ p = F∆t
Unit is N s
Practice
A 20 N force acts on a 2 kg mass for 10 seconds.
What is the impulse?
What is the change in velocity of the mass?