Physics 1: Energy 2
Kalamazoo Valley Community College
Work: A push or pull across a distance. 𝑊 = 𝐹 ∙ 𝑑
unit: Joule.
Potential Work: A push or pull which could be
applied across a distance.
Energy is a way of describing work an object does.
There are many different forms which energy can
take and different equations to describe energy. All
of these forms are in some way traced back to
𝐹 ∙ 𝑑.
Energy can be converted from one type to another.
Short List of Energy Types
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Work (W)= 𝐹 ∙ 𝑑
Kinetic Energy (KE) = 12𝑚∙𝑣 2
Rotational Kinetic Energy (KEr) = 12𝐼∙𝜔2
Gravitational Potential (PEg) = 𝑚𝑔ℎ
Spring Potential (PEs) = 12𝑘∙𝑥 2
Electrical Potential Energy (PEe) = 𝑞𝐸
Heat (Q) = 𝑚𝑐∆𝑇
Internal Energy (U)
There are many other types of Energy and we are always looking for new ones.
Example
A block starts from rest and slides 0.750m to the
bottom of an inclined plane at 23.0°. The block
has a mass of 1.22kg. The coefficient of friction
between the block and the incline is 0.25. What
is the speed of the block at the bottom of the
incline?
START
0.75m
23°
END
By including friction the problem has
some initial preparation before we can
start using the energy method. Any
time friction is mentioned we
automatically need a Free-Body
Diagram.
Draw the forces acting on the Block.
We really only care about solving for
the value of the normal force (n).
𝐹𝑦 = 0
𝑛 − 𝑚𝑔𝑐𝑜𝑠 23° = 0
𝑛 = 𝑚𝑔𝑐𝑜𝑠 23°
n
f = mn
23°
W=mg
Conservation of Energy:
We are going to look at the block and ask yes or
no questions the different energies listed earlier.
The Left side of the equation is reserved for
energy which is used on the block while the
right will be for energy spent by the block.
LEFT
Work (W)= 𝐹 ∙ 𝑑
Kinetic Energy (KE) = 12𝑚∙𝑣 2
Rotational Kinetic Energy (KEr) = 12𝐼∙𝜔2
Gravitational Potential (PEg) = 𝑚𝑔ℎ
Spring Potential (PEs) = 12𝑘∙𝑥 2
RIGHT
=
Work (W)= 𝑓 ∙ 𝑑
Kinetic Energy (KE) = 12𝑚∙𝑣 2
Rotational Kinetic Energy (KEr) = 12𝐼∙𝜔2
Gravitational Potential (PEg) = 𝑚𝑔ℎ
Spring Potential (PEs) = 12𝑘∙𝑥 2
LEFT
RIGHT
Work (W): Are there any push/pulls helping the block?
KE: Is the block moving at the start of the problem?
KEr: Is the block rotating at the start of the problem?
PEg: Will the block fall lower than were it started?
PEs: Did a spring push the block?
Work (W): Are there any push/pulls against the block?
KE: Is the block moving at the end of the problem?
KEr: Is the block rotating at the end of the problem?
PEg: Will the block end up higher than were it started?
PEs: Did a spring slow the block?
Try answer YES or NO to each question. If you answer YES write the equation down.
You will build the equations this way.
Since the block starts from rest we answer NO to moving and rotating on the left side.
The block is moving at the end of the problem, so we write KE on the right side. There
are no springs mentioned in the problem description so we say NO on the left and
right side. There are no forces on the left side giving the block energy and on the right
side friction slows us down.
𝑃𝐸𝑔 = 𝐾𝐸 + 𝑓 ∙ 𝑑
Normal force
From FBD
0.75m
h
𝑚𝑔ℎ = 12𝑚𝑣 2 + 𝜇𝑛 ∙ 𝑑
d: Distance the friction
Force travels
23°
x
ℎ = 0.75𝑚 ∙ sin⁡(23°)
h: height change of
the block.
ℎ = 0.293𝑚
𝑚𝑔ℎ = 12𝑚𝑣 2 + 𝜇𝑚𝑔𝑐𝑜𝑠 23° ∙ 𝑑
9.80𝑠𝑚2 ∙ 0.293𝑚 = 12𝑣 2 + 0.25 ∙ 9.80𝑠𝑚2 ∙ 𝑐𝑜𝑠 23° ∙ 0.75𝑚
9.80𝑠𝑚2 ∙ 0.293𝑚 = 12𝑣 2 + 0.25 ∙ 9.80𝑠𝑚2 ∙ 𝑐𝑜𝑠 23° ∙ 0.75𝑚
2
2
1 2
𝑚
2.871𝑚
=
𝑣
+
1.691
2
2
𝑠
𝑠2
2
𝑣 2 = 2.360𝑚
𝑠2
𝑣 = ±1.54𝑚
𝑠
The downside of the energy method is deciding which sign on velocity is the correct one.
Unlike Kinematics and Forces, Energy is a scalar and thus blind to direction. We have to
look at the picture.
The block slides along the incline. The velocity vector must be pointed down the incline.
𝑣 = 1.54𝑚𝑠∠ − 23°