Conservation of Energy Review
Work
-
Work is done when a force causes a displacement of the object
Work is only done when components of force are parallel to displacement
The energy of the object has changed is the best evidence that work has been done on or by an
object.
𝑊 = 𝐹𝑛𝑒𝑡 𝑑𝑐𝑜𝑠Ɵ
-
The sign of the work is important:
o Positive work can cause an object to speed up.
o Negative work can cause and object to slow down.
Kinetic Energy
-
Kinetic energy is the energy of an object that is due to the object’s motion
Kinetic energy depends on speed and mass.
1
𝐾𝐸 = 𝑚𝑣 2
2
-
The Work-Kinetic Energy Theorem - the net work done on a body equals its change in kinetic energy.
𝑊𝑛𝑒𝑡 = ∆𝐾𝐸
𝑊𝑛𝑒𝑡 =
1
1
𝑚𝑣𝑓2 − 𝑚𝑣𝑖2
2
2
Potential Energy
-
The energy associated with an object because of its interaction with the environment
Gravitational Potential Energy – the energy associated with an object’s position relative to a
gravitational source.
𝑃𝐸 = 𝑚𝑔ℎ
o
o
-
Gravitational potential energy is the potential energy stored in the gravitational fields of
interacting bodies
Gravitational potential energy depends on the height from a zero level.
Elastic Potential Energy – the energy available for use when a
deformed elastic object returns to its original configuration.
1
𝑃𝐸𝑒𝑙𝑎𝑠𝑡𝑖𝑐 = 𝑘𝑥 2
2
o
Spring Constant – k – (or force constant) a parameter that is a
measure of a spring’s resistance to being compressed or
stretched
-
Energies are represented in a roller coaster car at various
positions on the track.
A - None
B - PE
C - PE + KE
D - KE
Conservation of Energy
-
Mechanical Energy – the sum of kinetic energy and all forms of potential energy.
o Mechanical energy is often conserved
o Mechanical energy is not conserved in the presence of friction
𝑀𝐸 = 𝐾𝐸 + 𝑃𝐸
𝑀𝐸𝑖 = 𝑀𝐸𝑓
1
1
𝑚𝑣𝑖2 + 𝑚𝑔ℎ𝑖 = 𝑚𝑣𝑓2 + 𝑚𝑔ℎ𝑓
2
2
-
Mechanical Energy includes:
Pendulum
Spring
Ramp
Roller coaster
Ball rolling down or up a hill
Throwing a ball into the air
-
Non-Mechanical Energy includes:
Chemical
Light
Heat (thermal)
Nuclear
Electrical
Atomic
-
A quantity that measures the rate at which work is done or the rate of energy transfer by any method.
o Amount of work per unit of time – the rate of which work is done
Power
𝑃 = 𝑊/∆𝑡
𝑃 = 𝐹𝑣