1. Work
Work – The product of the magnitudes of the component of force along the direction of displacement and the displacement.
Or, more simply, a force that causes a displacement of an object does work on the object.
Work is done only when components of a force are parallel to a displacement.
Components of a force perpendicular to a displacement do not do work.
Net Work Done by a Constant Net Force
Wnet = Fnet d(cos θ)
net work = net force x displacement x cosine of the angle between them

2. Work (cont.) Work has dimensions of force times length.
In the SI system, work has a unit of newtons times meters (N · m), or joules (J), or (kg · m2/s2).
English or Standard unit of work is the foot · pound.
The joule is named for the British physicist James Prescott Joule who made major contributions to the understanding of energy, heat, and electricity.

3. Work (cont.) The sign of work is important:
Work is a scalar quantity that can be positive or negative.
Work is positive when the component of force is in the same direction as the displacement.
Lifting a box – force is upward, box moves upward.
Work is negative when the force is in the direction opposite the displacement.
Sliding a box – kinetic friction is opposite the displacement of the box. So kinetic friction does negative work on the box.

4. Power Power – The rate at which work is done or energy is transferred.
It is possible to do the same amount of work and different amounts of power.
Power Equation:
P = W/t
power = work ÷ time
The SI unit of power is (J/s) or the watt.
Alternate form of Power
P = Fv
power = force x speed

5. Example Problems
An appliance salesman pushes a refrigerator 2 meters across the floor by applying a force of 200 N. Find the work done.
Answer: W=Fd(cosθ) = 200N x 2m(cos 0°) = 400 J
A friend’s car is stuck on the ice. You push down on the car with a 100 N force to provide more friction for the tires (by way of increasing the normal force), allowing the car’s tires to propel it 5 meters forward onto less slippery ground. How much work did you do?
Answer: W=Fd(cosθ) = 100 N x 5 m(cos 90°) = 0 J

6. Example problems
Rob and Peter push a couch 5 m across the floor by applying a 200 N force for 8 seconds. What power did they supply?
Answer: P = W/t = Fd(cosθ)/t = 200 N x 5 m (cos0°) / 8s = 125 W

7. Energy Energy – The ability to do work.
Kinetic Energy – The energy of an object due to its motion.
Kinetic energy depends on speed and mass.
Kinetic Energy Equation:
KE = ½ mv2
kinetic energy = ½ x mass x (speed)2
Kinetic energy is a scalar quantity.
The SI unit of kinetic energy (and all other forms of energy) is the joule (J).

8. Energy (cont.)
Work-Kinetic Energy Theorem – The net work done on an object is equal to the change in the kinetic energy of the object.
Work-Kinetic Energy Theorem Equation:
Wnet = ∆KE
net work = change in kinetic energy
Expanded form:
Wnet = ½ mv2f - ½ mv2i

9. Potential Energy
Potential Energy – The energy associated with an object due to the position of the object.
Gravitational potential energy depends on height from a zero level.
Example: A book on your desk. What is its PE relative to the floor? What is its PE relative to the desk?
Gravitational Potential Energy Equation:
PEg = mgh
Gravitational potential energy = mass x free-fall acceleration x height
PEg depends on both the height and the free-fall acceleration, neither of which is a property of an object.

10. Elastic Potential Energy
Elastic Potential Energy – The potential energy in a stretched or compressed elastic object.
Elastic potential energy depends on distance compressed or stretched.
The length of a spring when no external forces are acting on it is called the relaxed length.
Spring Constant – A parameter that expresses how resistant a spring is to being compressed or stretched.
It is represented by the symbol k.

11. Elastic Potential Energy (cont.)
Elastic Potential Energy Equation:
PEelastic = ½ kx2
elastic potential energy = ½ x spring constant x (distance compressed or stretched)2

12. Conserved Quantities
Mechanical Energy – The sum of the kinetic energy and all forms of potential energy.
Mechanical Energy Equation:
MEi = MEf or
½ mv2i + mghi = ½ mv2f + mghf

13. Momentum
Momentum – The product of an object’s mass and the object’s velocity.
Momentum Equation:
p = mv
momentum = mass x velocity
The units of momentum are kg • m/s.
Momentum is a vector quantity.

14. Impulse
Impulse – The product of the constant applied force and the time interval during which the force is applied.
Impulse Equation :
I = Δp = FΔt
Impulse = change in momentum = Force x time
Units are N•s which equal kg • m/s.

15. Conservation of momentum
Conservation of Momentum – In the absence of an external force, the momentum of a system remains unchanged.
Conservation of Momentum Equation:
m1v1 + m2v2 = m1v1’ + m2v2’
Elastic Collision – In an elastic collision, two objects return to their original shapes and move away from the collision separately.
Inelastic Collision – In an inelastic collision, two objects stick together and move as one mass after the collision.

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Now enjoy your evening!