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PHYS 2101 – Fall 2023
Lab 7
ENERGY
Fig. 1: Investigating Energy Exchanges - Kinetic Energy and Gravitational
Potential Energy
Fall
2023
PHYS 2101 – Fall 2023
Objectives:
At the end of this lab, students should be able to
1)
calculate different forms of mechanical energy, and
2)
verify the law of conservation of energy.
1. Introduction:
The law of conservation of energy states that the total amount of energy in an
isolated system
remains constant. In other words, Energy can neither be created nor destroyed but can change its
forms.
The total energy
E
of a system (the sum of its mechanical energy and its internal energies,
including thermal energy) can change only by the amounts of energy that are transferred to or
from the system. If work
W
is done on the system, then
W = ΔE = ΔE
mech
+ ΔE
th
+ ΔE
int
(7.1)
If the system is isolated (i.e., W = 0):
ΔE
mech
+ ΔE
th
+ ΔE
int
= 0
(7.2)
The
skate-park
is an excellent example of the conservation of energy. For the isolated skate-
track-Earth system, the law of conservation of energy equation has the form
ΔE
mech
+ ΔE
th
= 0
(7.3)
The unit of Energy is Joules
(J
) in the
SI
system.
1.1 Mechanical Energy
: The mechanical energy
E
mec
h
of a system is the sum of its kinetic
energy K and its potential energy, U;
E
mech
= K + U
(7.4)
The conservation of mechanical energy can be written as;
ΔE
mech
= ΔK + ΔU = 0.
(7.5)
It can also be rewritten as
K
1
+ U
1
= K
2
+ U
2
(7.6)
where the subscript refers to different instants during an energy transfer process.
1.2 Gravitational Potential Energy
:
The potential energy associated with a system
consisting of Earth and a nearby particle is gravitational potential energy. If the particle moves
from y
1
to height y
2
, the change in gravitational potential energy of the particle-Earth system is
ΔU = mg (y
2
– y
1
) = mgΔy.
(7.7)
1.3 Kinetic Energy
:
The kinetic energy is associated with the state of motion of an object. If
an object changes its speed from v
1
to v
2
, the change in kinetic energy is
ΔK = K
2
– K
1
= ½ mv
2
2
- ½ mv
1
2
(7.8)
Fall
2023
PHYS 2101 – Fall 2023
2. Procedure
Please click here (
https://excelschools.net/en/simulation/energy-skate-park.html
)
to download the
PhET simulation link for
Energy Skate Park
.
Take some time and
play with the skater and his
track
. It helps to practice with the following features and controls.
Track selector
: click on ‘
Tracks’ located on the top right (Next to ‘File’)
and select from the
drop-down menu. For example, the “
Double well (Roller Coaster)
” shown above.
Reset
(located on the top right): This rests the simulation to default values and sets the track to
friction parabola track.
Skater selector
: clicking on ‘
Choose skater…’
will allow you to choose a skateboarder with a
different mass option.
Measuring Tape:
Check the ‘
Measuring Tape Bo
x’ when you want to make measurements.
Drag the left end of the tape measure to where you start your measurement and then drag the
right end to the final location. To make a reference horizontal line to your measurement, check
the
potential energy reference
box and drag the
blue line
you see on the screen to the initial
position.
Graph Selector:
If you would like to observe graphs that depict the relationships among
potential, kinetic, and thermal energy
of the simulation, click the buttons under the
Energy Graphs.
The types of graphs are shown above. You can also add
pie graphs
by
checking the
show pie chart
box. These graphs can be shown
with or without Thermal energy
.
Gravity:
you may change the gravitational force by changing the location or the sliding bar
underneath the Gravity box.
Additional Features
: Clicking the C
lear Heat
makes the track frictionless. You can also edit
the track friction and the skater mass using the
Track friction
and
Edit Skater
buttons. You can
also control the speed of the skater using the slide bar under the screen.
Whenever you are done playing make sure you reset the simulation and start the steps below:
Part I: Parabolic Track
1.
Click Reset and click on
‘Bar Graph’
,
‘Energy vs. Position’
, and
‘Energy vs. Time’
.
Observe the energy bars as the skater moves back and forth.
As the skater descends, his kinetic energy (green) ____________ and his potential energy
(blue)_________. The ‘Total’ energy bar_____________. [3 Points]
2.
Check the ‘
Measuring Tape box’
(please refer procedure section about how to use
measuring tape). Considering the bottom of the parabola as a reference line, measure the
maximum height (
h
) the skater climbs
h
= ________________ [1 Point]
Fall
2023
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PHYS 2101 – Fall 2023
3.
Observe the
‘Energy vs. time graph’
as the skater moves back and forth. The
gravitational potential energy at the maximum height to which the skater reaches is equal
to _____ Joules. [1 Point]
4.
Apply the principle of conservation of mechanical energy to calculate the skater’s speed
at the lowest point of the parabola. Show your work to get full credit. [4 Points]
5.
Replace the skateboarder with a Bulldog and repeat steps 2, 3, and 4. [6 Points]
a.
h = ______ m
b.
gravitational potential energy = ______ Joules
c.
speed = _____ m/s
6.
Is the law of conservation of energy affected by the mass of the skater?
Yes/no? [1 Point]
7.
Now click
Reset
.
Check the
‘potential Energy Reference’
box.
Drag the reference line at
the lowest point of the parabola and observe the ‘
Energy versus Position graph
’ as the
skater moves back and forth.
a.
Pause the simulation at the bottom of the parabola and record the following
values: [3 Points]
i.
Kinetic energy = ______Joules
ii.
Potential energy = ______Joules
iii.
Total energy= ______ Joules
b.
Play the simulation and then pause it at the maximum height. Record the
following: [3 Points]
i.
Kinetic energy = ______Joules
ii.
Potential energy = ______Joules
iii.
Total energy= ________ Joules
What do you conclude about the values of different types of mechanical energies at top and
bottom of its path? [2 Points]
8.
Apply the following settings:
a.
Stop the simulation.
b.
Click ‘
Reset
’
then ‘
Return skater
’
buttons.
c.
Click the
‘Track friction’
and adjust the coefficient of friction to the one-eighth
mark on the slide.
Fall
2023
PHYS 2101 – Fall 2023
d.
Open the
‘Energy versus Time’
graph and click on the ‘Stop’ button located in the
graph.
e.
Drag the skater to the top of the parabola and release him. Press ‘
Go
’.
f.
Run the simulation for 20 seconds
9.
What are the energies at 12 seconds and 17 seconds [3 Points]
a.
at 12 seconds: K = ________ J
U = ________ J
E
th
= ________ J
b.
at 17 seconds: K = ________ J
U = ________ J
E
th
= ________ J
10. Calculate the change and total energies between the 12
th
and 17
th
second. [5 Points]
a.
Δ
K = ________ J
Δ
U = ________ J
Δ
E
th
= ________ J
b.
Total change in Energy:
Δ
E =
Δ
K +
Δ
U +
Δ
E
th
= _________ J
11. What are the two times when the
KE
and
PE
of the skater are the same? Where do you
think the skater is along its path when this happens?
[4 Points]
Part II: Double Well (Roller Coaster)
Fig. 2
1.
Click the ‘
Reset’
and ‘
Return Skater’
buttons. From ‘
Tracks
’ select ‘
Double Well
(Roller Coaster)
’. Check the
‘Potential Energy Reference’
box and drag the reference
Fall
2023
PHYS 2101 – Fall 2023
line to the position as shown in Figure 2 above. Measure the height of each control point
(1,2,3,4 and 5 in the figure above) from the reference line. Calculate the potential (U),
kinetic (K), and total (E) energy of the skater at these points (assuming the track is
frictionless).
Show your calculation for (a) and (c) only
. [6 Points]
a.
At point 1:
h
1
= ___ m.
U
1
= ______J
K
1
= ______J
E
1
= ______ J
b.
At point 2:
h
2
= ___ m.
U
2
= ______J
K
2
= ______J
E
2
= ______ J
c.
At point 3:
h
3
= ___ m.
U
3
= ______J
K
3
= ______J
E
3
= ______ J
d.
At point 4:
h
4
= ___ m.
U
4
= ______J
K
4
= ______J
E
4
= ______ J
2.
Calculate the speeds at control points 3 and 4 using the kinetic energy you calculated in
the previous step. Show your work. [4 Points]
a.
The skaters speed at point 3:
v
3
= _______m/s
b.
The skaters speed at point 4:
v
4
= _______m/s
3.
Now open the
Energy vs Position Graph
and read the potential (U), kinetic(K), and
total (E) energies at the control points [4 Points]
a.
At point 1:
U
1
= ______J
K
1
= ______J
E
1
= ______ J
b.
At point 2:
U
2
= ______J
K
2
= ______J
E
2
= ______ J
c.
At point 3:
U
3
= ______J
K
3
= ______J
E
3
= ______ J
d.
At point 4:
U
4
= ______J
K
4
= ______J
E
4
= ______ J
4.
Calculate the heights at each of the control points using the information from step 3.
Show your work. [5 Points]
Fall
2023
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PHYS 2101 – Fall 2023
a.
h
1
= ____ m,
h
2
= ____ m,
h
3
= ____ m,
h
4
= ____ m,
h
5
= ___.
5.
How does the shape of potential and kinetic energies relate to the shape of the track? [2
Points]
a.
Potential energy to the track:
_____________________________________
b.
Kinetic energy to the track: ________________________________________
6.
If you change the location to the
Moon
instead of
Earth
, will the shape of the energies
change? If not, what will change if any? [2 Points]
7.
Apply the following settings for the simulation to answer the proceeded questions.
a.
Stop the simulation.
b.
Click
‘Reset’
followed by the ‘
Return skater
’
button. Choose the ‘
Double
Well
Roller Coaster’
track.
c.
Adjust the
coefficient of friction
to the
one-eighth
mark on the slide
d.
Open the
Energy versus Time Graph
. Click on “
Stop
’ and then “
Clear
”
button on the graph.
e.
Drag the skater to the top of the roller coaster
and then press on ‘
Go
!’.
f.
Run the simulation for 20 seconds
8.
What are the energies at 9 seconds and 16 seconds? [4 Points]
a.
at the 9
th
second:
K = ________ J
U = ________ J
E
th
= ________ J
b.
at the 16
th
second: K = ________ J
U = ________ J
E
th
= ________ J
9.
Calculate the change and total energies between the 9
th
and 16
th
-second timestamp. E
th
is
thermal energy [4 Points]
a.
Δ
K = ________ J
Δ
U = ________ J
Δ
E
th
= ________ J
b.
Total change in Energy:
Δ
E =
Δ
K +
Δ
U +
Δ
E
th
= _________ J
10. Pick any time between
1 and 9
seconds
and record the values of
K, U, E
th
,
and Total
E
. Describe how they are related. [2 Points]
11. Pick any time other than that you chose for Step 10 and repeat the process. Do the
relations you found in 10 still hold good? Why/why not does this relation hold/ not
hold? [2 Points]
12. Why do you think thermal energy just keeps on rising? [1 Point]
Fall
2023
PHYS 2101 – Fall 2023
Part III:
Create your own Track
[where a skater can make a loop (a sample figure
below) and then flies off] (8 Points)
You can keep adding extra tracks by dragging
“Tracks” located on the top right inside the
blue rectangle to the screen. Connect them by
connecting the red circles.
Take a screenshot of your track and paste it
below.
For the track, you created, calculate the
velocity at the top and bottom of the loop and
the speed by which the skater flies off from the
edge. Show all the measurements and
calculations you performed to get full credit.
Fall
2023
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Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY