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Equations:
p = mv (momentum = mass x velocity)
J = F x delta t = delta p (Impulse = Force x delta time = delta momentum)
m1vi + m2vi = m1vf + m2vf (mass 1 x initial velocity + mass 2 x initial velocity = mass 1 x final velocity + mass 2 x final velocity)

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Equations:
Wf = umgd = (1/2)mv(final)^2 - (1/2)mv(initial)^2 (Frictional Work = u x mass x gravity x distance = (1/2) x mass x final velocity ^2  - (1/2) x mass x initial velocity ^2)
W = delta E (Work = final Energy - initial Energy)
W = Fd (Work = Force x distance)

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What do I know about this concept?
The final minus the initial momentum in a situation is equal to the impulse. Both momentum and impulse are vectors, meaning they are dependent on signs and direction. Momentum can be defined as the "persistence of motion," whereas impulse is the "change in momentum." Similarly to energy, the Law of Conservation of Momentum states that momentum can be neither created nor destroyed. Three examples of momentum are (1) a bike rolling down a street, (2) a bowling ball rolling down and alley, and (3) a man running through a finish line. Momentum and impulse exist in two types of collisions: inelastic and elastic. In an inelastic collision, the object in motion sticks upon impact; in an elastic collision, the object in motion bounces back upon impact.

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Problem:
A 10 kg cart is rolling down a hill at 15 m/s, and it slows to 5 m/s at the bottom of the hill. What is its impulse?
-100 kg m/s

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Equations:
W = Fd (Work = Force x distance)
Ek = (1/2)mv^2 (Kinetic Energy = (1/2) x mass x velocity^2)
Ep = mgh (Potential Energy = mass x gravity x height)
EP = (1/2)kx^2 (Elastic Potential = (1/2) x spring constant x distance^2)
P = delta Energy / delta time = work / delta time (Power = delta Energy / delta time = work / delta time)
E = P x delta t (Transferred energy = power x delta time)

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What do I know about this concept?
Work can be defined as the "change in energy." When calculating Work, you can cancel out what doesn't apply to the situation: for example, velocity can be cancelled if the object is not in motion. The difference between Work and Energy is (1) Energy is the ability to do work, (2) Work must be done in order for Energy to be transferred between objects, and (3) Work must be done for Energy to change from one form to another.

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How do we use these in life?
Momentum and impulse can be best seen in car wrecks. If someone were to rear end another car ahead of them, for example, the damage would be dependent on each car's mass and velocity. If a small car hit something going slowly, the damage wouldn't be terrible; however, if a large car hit something going quickly, the damage would be much greater.

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Equations:
Ff = uk x Fn (Kinetic friction = Coefficient of Kinetic friction x Normal Force)
Ff = us x Fn (Static friction = Coefficient of Static friction x Normal force)
uk = Ff/Fn (Coefficient of Kinetic friction = Frictional force / Normal force)

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What do I know about this concept?
Energy can be defined as "movement" or "the ability to do work." Energy exists in 6 forms: kinetic, gravitational potential, elastic potential, thermal, electrical, and chemical. Examples of each are as follows: a car moving down a road is thermal, weightlifting is gravitational potential, bungee jumping is elastic potential, ice melting is thermal, static electricity is electrical, and propane is chemical. Energy is measured in Joules, which is written as "J." The difference between Work and Energy is (1) Energy is the ability to do work, (2) Work must be done in order for Energy to be transferred between objects, and (3) Work must be done for Energy to change from one form to another. The Law of Conservation of Energy states that Energy can be neither created nor destroyed in an isolated system, only converted.

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Problem:
A car with a mass of 1,000 kg is going 50 m/s. How far does it go if it running on a 100 N force?
12,500 m

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Problem:
A bike is moving down a road at 20 m/s. The bike weighs 10 kg, and its rider weighs 60 kg. What is their Kinetic Energy?
14,000 J

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What do I know about these concepts?
Friction exists everywhere. A world without friction is only imaginable, not attainable. Static friction is stationary, whereas kinetic friction is in motion. Examples of static friction include a heavy box stuck on the ground, a pencil lying on a desk, or a person standing still. Examples of kinetic friction include air resistance, a ball rolling down a hill, or an ice skater.

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How do we use this in life?
Energy exists everywhere. There is nothing without energy. Any movement is fueled by energy. An example of energy in everyday life is working out. Multiple forms of energy are exerted in a work out: gravitational potential when lifting weights, kinetic when running, and thermal and chemical within your body.

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Problem:
A box is sliding across the ice with a normal force of 10 N. The coefficient of kinetic friction is 0.5. How much kinetic friction is acting upon the box?
5 Newtons

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How do we use these in life?
Friction is something we face every day. It exists everywhere in the material world- it is only absent in an imaginary, perfect world. An example of friction could be pushing a heavy box out of your way. When it is stationary, you are fighting static friction. It will remain static until the applied force is greater than the static friction. Once the box is moving, the static friction converts to kinetic friction. It will continue to move until the applied force is removed or it is acted upon by another outside force (such as a wall, gravity, etc).

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Equations:
F=ma (Force = Mass x Acceleration)
F=mg (Force = Mass x gravity (9.8m/s^2))
F=(-k)x (Force of a spring = Spring constant x Displacement)
a=v/t (Acceleration = Velocity / Time)
v=d/t (Velocity = Distance / Time)

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What do I know about these concepts?
These laws were first established by Isaac Newton in 1687. Newton, a brilliant scientist and mathematician, is known for his work with gravity, motion, and force (among other concepts). Newton's Three Laws of Motion describe all moving objects, and they go as follows:
(1) An object in motion will remain in motion unless acted upon by an outside force, and an object at rest will remain at rest unless acted upon by an outside force
(2) Force = Mass x Acceleration
(3) Every action has an equal and opposite reaction
These Laws have been tested and tried for nearly 350 years, and they have proven themselves to be true to this day.

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Problem:
A 1,200 kg car initially traveling at 20 m/s hits a wall. The driver notices the wall 5 seconds before impact and slows to 5 m/s. With what force does the car hit the wall?
3,600 Newtons

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How do we use these in life?
Newton's 3 Laws describe motion. We experience motion all around us. For example, the cars we drive are in motion unless acted upon by an outside force (i.e. the breaks, another car, etc). When a car is in a collision, the force of its hit is its mass multiplied by its acceleration. In order to stop a car, the breaks must apply a force equal and opposite to the acceleration.

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Video:

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How do we use this in life?
An example of work in everyday life is rolling a bowling ball down and alley. Force must be exerted to back the bowling ball, then the ball with go a distance and speed dependent on the force.

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