Physics 1A
Lecture 5B
"If the only tool you have is a hammer, every
problem looks like a nail.”
--Abraham Maslow
Potential Energy
Another type of energy is potential energy.
Kinetic energy quantifies motion.
Potential energy (PE or U) is the amount of stored
energy you have that can perform work or be
transferred to kinetic energy.
Potential Energy is also measured in Joules.
Potential Energy is also a state variable, it only
depends on the initial and final values (it is not
path dependent).
Potential Energy
Work can also go into changing potential energy.
Gravitational potential energy changes as you change
the height of an object.
Near the surface of the Earth we calculate the change
in gravitational potential energy to be:
ΔPE = mg (yf - yi) = mgΔy
If I drop a 1kg mass from 6m to 1m, then ΔPE
becomes (up is +y):
ΔPE = mgΔy = (1kg)(9.8N/kg)(1m - 6m) = -49J
Potential Energy
Potential energy is only useful if you have a reference
point from which to measure.
For example, if I lift this eraser above the table. I can
state that it has 5,278,159,314 Joules of energy above
the core of the Earth.
This value is only useful if I can release that energy.
But if we make a reference point of zero Joules at the
table top, we can measure PE with respect to that.
This is because absolute PE means very little, only the
change in PE (ΔPE) will be of importance.
In Class Question
Which of the following forces performs the greatest
amount of work on the object (which only moves in x)?
10N
8N
F
F
90o
Δx
A) The 10N force.
60o
F
Δx
Δx
3N
0o
B) The 8N force.
C) The 3N force.
D) All three forces perform the same amount of work on
the object.
Conservative Forces
A conservative force is one that performs work
that transfers energy between useable systems
and is reversible.
For example, if I drop an apple, the gravitational
force performs work on the apple.
Gravitational force transfers PE in the apple to KE
in the apple. It is a conservative force, energy is
not lost to other systems.
A non-conservative force is one that transfers
energy out of a particular system and is not
reversible.
Conservative Forces
For example, an airplane flies through the air with a
drag force on it.
The drag force performs negative work on the
airplane transferring energy into heating the air,
making sound, moving air, etc.
You can’t get that energy back to the airplane.
Energy is not destroyed, it is just not in a useable
form.
The airplane can’t use the sound waves that the drag
force creates to get back to its previous position.
Conservative Forces
How can you tell, in general, if a force is
conservative or not?
The easiest way is to have the force act over a
closed path.
If the force is conservative:
W1 + W2 = 0
If the force in nonconservative:
W1 + W2 ≠ 0
In other words, the work
due to a conservative force
is path independent.
Conservative
Forces
Examples of conservative forces include:
Gravity
Electromagnetic forces
Spring forces
Potential energy is another way of looking at the
work done by conservative forces.
Conservative forces transfer energy from potential
energy to kinetic energy (or vice versa).
Examples of nonconservative forces include:
kinetic friction
air drag
Mechanical Energy
When dealing with macroscopic systems (large
objects) it is nice to deal with mechanical energy:
Emec = KE + PE
We can easily observe changes in Emec (as opposed
to changes in internal energy).
In order to change Emec for a system, we need to
perform some kind of work on the system due to
an external force.
By lifting a ball, I have changed the potential
energy of the system (ball and Earth) and thus
the mechanical energy of the system.
Mechanical Energy
In an isolated system where conservative forces
only cause energy changes, Emec is constant for the
system.
But in this system KE and PE can change.
This is the principle of conservation of mechanical
energy. In equation form:
If Wnc = 0,
ΔEmec = ΔKE + ΔPE = 0
Thus, if the work done on the system is zero, then
for two time periods 1 and 2:
KE1 + PE1 = KE2 + PE2
Mechanical Energy
Example
A block slides across a horizontal, frictionless
floor with an initial velocity of 3.0m/s, it slides
up a ramp which makes a 30o angle to the
horizontal floor. What distance will it travel up
the ramp?
vo
30o
Δy
Answer
First, you must define a coordinate system.
Let’s choose the upward direction as positive and
make the floor to be y = 0.
Mechanical
Energy
Answer
Next, use conservation of mechanical energy:
While on the floor:
Efloor = PE1 + KE1 = 0 + KE1 = (1/2)mvo2
While at its maximum height:
Emax = PE2 + KE2 = PE2 + 0 = mgΔy
Since no energy is taken away from the system
between the initial and final points:
Mechanical
Energy
Answer
But this is not the distance up the ramp.
We need to turn to trigonometry to solve this
problem.
Make a triangle to solve:
d
30o
Δy = 0.46m
Clicker Question 5B-2
Blocks A and B, of equal mass, start from rest and
slide down the two frictionless ramps shown below.
Their speeds at the bottom are vA and vB. Which of
the following equations regarding their speeds is
true?
B
A
1m
1m
30o
A) vA > vB
B) vA = vB
C) vA < vB
60o
For Next Time (FNT)
Keep working on the HW for
Chapter 5.
Finish Reading Chapter 5.