Conservation Laws
IF I GAVE YOU $1, HOW MANY OF THE
FOLLOWING COULD YOU EXCHANGE THE
DOLLAR FOR?
a. QUARTERS
b. NICKELS
c. DIMES
Law of Conservation of Energy
 Energy cannot be created nor destroyed; it can only
change form.
 Energy is the ability of an object to do work
 Energy has MANY different forms:






Kinetic
Potential
Thermal
Chemical
Electric
Elastic
Energy Transformations
 Example: Cat dropped from a 15 m high building!
Energy Transformations
 Example: Cat sitting in a car on the roller coaster
below!
Law of Conservation of Mass
 Mass in a system remains constant.
 Examples :
 An astronaut here vs. the SAME astronaut on the moon
 One cup of water placed in the freezer overnight
 The same cup of water placed on the stove
 Ball of clay, broken apart
Law of Conservation of Momentum
 When objects interact, momentum remains constant
 Momentum is changed by the interaction of forces!
 This topic will be explored more in the near future…
Kinetic Energy (KE)
 Defined as the energy of motion
 If an object is moving, it has kinetic energy!
 If an object is not moving, it does NOT!
 Example: running cat, jogging football player, falling
cat, walking dog, etc
 SI unit is the Joule (J), and it is a scalar quantity
 Problem: If a 1200 g cat moves
at 0.73 m/s, what is
its kinetic energy?
Gravitational Potential Energy (U or PEg)
 Defined as stored energy due to an object’s position
above some reference point.
 Example: If a cat stands on a chair, it stores energy
that could be used if it jumps off and falls to the
floor!


If the same cat stands on the top of the stadium, it has MORE
stored energy, because it is HIGHER off the ground!
In BOTH of these examples, the floor, or ground is the
reference point. (The reference point has ZERO PE)
Gravitational PE, continued…
 m – object mass in kg
g – gravitational acceleration (9.81 m/s2)
h – height above the reference point, in meters
 Potential energy is a scalar quantity, with units of
Joules (J)

You CAN have a negative PE if you are UNDER the reference
point!
 If a 1700 g cat rests at the top of a 12.5 meter high
stadium (before being pushed off by a disgruntled
physics student with angry tendencies toward cats!)
What is its PEg?
Elastic Potential Energy (EPE)
 Defined as the energy stored when a spring is
compressed or stretched.
 EPE is a scalar quantity and has units of Joules (J)
 k – spring constant in N/m
x – stretched or compresses distance from
equilibrium, in meters
EPE, continued…
 A 200 g mass hangs from a spring, stretching the
spring 15.5 cm. What is the spring constant of the
spring?
 What is the EPE of the same spring?
Mechanical Energy (ME)
 Defined as the sum of all potential energies and the
kinetic energy of an object.
 Mechanical energy is conserved EXCEPT when
friction is present BECAUSE

Some of the PE and KE turns into THERMAL energy (Q)
ME, continued…
 ME is a grouping of energy, so it is a scalar quantity
with units of Joules (J)
 A 1.5 kg cat runs at 3.75 m/s off a 15.5 m high
rooftop. While it is running, what is its Mechanical
Energy?
Problem Solving…
 In the above problem, with what velocity would the
cat hit the ground?
Problem Solving…
 A 1500 kg roller coaster car starts at the top of hill A,
which is 55 meters off the ground. Hill B is 32 meters
off the ground, and hill C is 22 meters off the ground.
What is the car’s speed when it reaches the top of
each hill?

Now we take a motion detector and MEASURE the velocities
on hills B and C. What would we discover, and why?
Problem Solving…
 A diver atop a 10.0 m high diving board drops into
the water below. As the diver hits the water, what is
her speed?
Problem Solving…
 A cat falls from a cliff into a large body of water. If
the cat hits the water with a speed of 22 m/s, how
high was the cliff?
Problem Solving…
 A girl is on a 1.5 m long swing. At the swing’s
maximum height, the swing makes a 25 degree angle
with the vertical. What is the swing’s speed at its
lowest point?
Work and Energy
 Work is defined as a force applied over a
displacement.
 The force and the displacement must be PARALLEL
in order or work to be done.

Ask yourself if the force helped to MOVE the object
 Work is a scalar quantity with units of Joules (J)
 This means it MUST be tied to energy!
 Work can be negative depending upon if it is Gaining energy
(+) or Losing energy (-)
Work, continued…
F
d
W
+
+
-
25N
11 N
θ=20 ⁰
d= 12 m
Work – Kinetic Energy Theorem
 Work done on an object causes it to MOVE!
 Thus, it has a change in kinetic energy!
 Actually, ANY energy form that can be converted to KE can be
used to do work o an object!
 In the previous problem,
if the box starts from rest,
what is its velocity at the end of the 12m?
Power (P)
 Defined as the rate of change of work or the rate of
change of energy.
 Power is a scalar
quantity with units of
Watts (W) where 1 Watt = 1 J/s
 32 lbs of water falls 75 m down a cliff. If it takes
2.5 seconds for the water to fall, what power could be
harnessed by the waterfall?
Efficiency (%eff)
 Defined as a ratio of the energy out of a system to the
energy put into a system.
 Scalar quantity with NO units! (Just written as a
percent)
 Can’t ever be 100% because EVERY system loses
some energy to the atmosphere!
Efficiency, continued…
 1550 J of work is done on a piston. In turn, the
piston does 545 J of work on the gas inside the
piston. What is the efficiency of the piston?