
 University of Virginia
 Physics Department

Change in Energy of a Cart on a Ramp (Version
B)
A Physical Science Activity


NOTE: There are two versions of this activity. Both use probes and graphing
calculators. Version A uses the CBL and a motion detector. Version B uses the
new CBR (Calculator Based Ranger) which is a TImade motion detector that does
not need the CBL. It has internal programs and is connected directly to the
TI83 or 83 plus calculator.
2003 Virginia SOLs
Objectives
Students will
 understand the quantitative relationships between total, potential, and
kinetic energies;
 measure and compare values of kinetic and potential energies;
 use the CBR calculator system to calculate instantaneous velocities;
 use the following skills: observing, comparing, inferring, predicting,
and experimenting with variables, and plotting graphs of variables.
See materials list for link to download CBR programs.
Motivation for
Learning
Demonstration: Energy of a Falling Ball


 Materials
Several different balls, preferably of the same size, but of different mass
(for example, a racquetball and a billiard ball).
Background and Procedure
We want the students to obtain a qualitative idea of the transfer of energy
from potential to kinetic. The harder the ball pushes on the hand that catches
it, the more kinetic energy it has at that point. If you drop a ball from one
hand to the other (one higher than the other), there are certain factors that
give the ball a different amount of kinetic energy at the end.
 If you change the height from which you drop a ball to a higher height,
then the ball will have more velocity and more kinetic energy at the end.
You can show this by having one hand as low as possible, and dropping a ball
from the height of your head, and then from as far up as you can reach, and
note the extra effort you exerted to stop the ball the second time. This shows
that the ball has more kinetic energy when it falls a greater distance.
 If you take a heavier ball and drop it from the same height as the other
lighter ball, there is also more kinetic energy and it requires more energy
to stop it. This shows that a heavier object at the same height as a lighter
one will have a greater potential energy.
Write down the equation for potential energy and show that the mass and height
are dependent variables (U = mgh, where U is potential energy, m is mass, g
is the acceleration of gravity, and h is the height of the object. Remember
that the zero of potential energy is arbitrary, so h can be measured from anywhere
you choose). Let the initial height be h_{1} and the
final height be h_{2}.
Write down the equation for kinetic energy (KE = ½ mv^{2})
and show that it is dependent on mass and speed of the object. You can show
that kinetic energy is higher with a greater speed by throwing the ball into
your other hand and expressing the extra effort you exert to stop the ball.
Similarly, show that for a constant speed, a more massive ball seems to have
more kinetic energy and requires more force or effort to catch.
Energy can neither be created nor destroyed, so the amount of energy lost as
potential energy when it was high up in the air should equal the kinetic energy
gained at the end of travel. This is what we will test in the experiment, whether
the term m*g*(h_{1}h_{2}) (where
(h_{1}h_{2}) is the actual
distance fallen) is equal to ½ *m*v^{2} (ending kinetic
energy).
In order to do this, we must measure the difference between starting and finishing
height Dh, the velocity at the end, and the mass
of the object. In order to calculate the velocity at the end we will use the
CBR. Since we want to slow down the whole process of the falling, we will use
a ramp and cart rather than a falling ball. We will use the CBR that connects
to the TI83 graphing calculator to follow the velocity patterns of the cart
as it descends the ramp.
Answers to Student Activity Questions
1. At the top of the hill you have lots of gravitational potential energy,
which is the energy stored in the gravitational force attracting you toward
the Earth.
2. As you loose altitude and pick up speed, more of your gravitational potential
energy is converted into kinetic energy. The amount of kinetic energy you gain
is exactly equal to the amount of potential energy you loose so that your total
energy remains constant.
3. The heavier cart will feel a larger gravitational force downward because
it has more mass, so it would seem like it would move faster. But, because it
has more mass than the other one, it will want to stay at rest more (that is,
its inertia is higher), so it takes more energy to move it. For these reasons
the heavier cart will go at the same speed as the lighter one.
Student
Activity
To print out the Student Copy only, click
here.
Materials
 Texas Instruments CBR Ranger motion detector.
 TI83 (or TI83 plus) graphing calculator with cable link. Also works with
TI82, but note that programs appropriate to the TI82 will need to be obtained.
 The following programs (Note: these programs can be downloaded for any
of the TI calculators at http://www.ti.com/calc/docs/cbr.htm
and clicking on your particular calculator in the CBR Program Archive.
 Program Ranger is in CBR.
 Wooden board (about 2 m long and at least 20 cm wide)
 Books or something large to prop board on
 Cart (could be a toy truck or physics cart, anything that rolls with little
friction).
 Large sponge or something soft to stop cart
 Mass scale (digital balance or triple beam balance)
Procedure
 Measure the mass of the cart on the mass scale.
 Connect the CBR unit to the TI Calculator with the unittounit link cable
using the I/O Ports located on the bottom edge of the units. Turn on units.
 Stack a few books (or something similar) beneath a wooden board, as shown
in the setup diagram. Place the motion detector at the top of the ramp and
position the dynamics cart at least 50 centimeters from the motion detector
(you will receive spurious results if the motion detector is closer than 50
cm to the moving object). Place the sponge or something soft at the bottom
of the ramp to catch the cart.
 Measure the height of release of the cart (you can experiment with average
value of height) and the height that the cart hits the sponge. It is important
that you subtract the height of the cart at the end of the trip from the original
height so that the change in height Dh is known to determine the potential
energy.
 Run the RANGER calculator program. Program the calculator to perform a
velocity vs. time measurement and for the initiation of data recording by
pressing the trigger button on the CBR. Start the velocity vs. time measurement
by pressing the trigger button and release the cart, making sure not to give
the cart any initial velocity when letting go. (Note: The RANGER program asks
for a time period that the experiment will run and calculates the reading
interval it needs to utilize all of its storage capacity for that given time.
Hence if a longer time is used then the intervals of measurement are long,
a short time gives smaller intervals. We found that a 5 s time interval works
well.)
 When the cart hits the stop, stop the calculator's measurements.
 Read off the velocity at the point it hit the stop (where the arrow is
pointing. The rapid oscillating values after this time are due to the bouncing
back and fourth of the cart after it hit and should be ignored).
 Calculate kinetic energy ( ½ mv^2) and potential energy loss {m*g*(h_{1}h2)}
and compare results. Perform this calculation for varying heights of the ramp.
Data Sheet
To print out the Data Sheet only, click here.
Trial #1 

Potential Energy Calculation 

Measurement: Mass of the cartM (kg)


Measurement: Original height (m) 

Measurement: Final height (m) 

Calculation: Difference in height h_{1}h_{2}
(m) 

Calculation: Difference in potential energy U = M*g*(h_{1}h_{2}) 

acceleration due to gravity, g = 9.8 m/s^{2} 

Kinetic Energy Calculation 

Calculator Measurement: Final velocityv (m/s) 

Calculation: Final kinetic energy
KE = (1/2)*M*v^{2}


Trial #2 

Potential Energy Calculation 

Measurement: Mass of the cartM (kg)


Measurement: Original height (m) 

Measurement: Final height (m) 

Calculation: Difference in height h_{1}h_{2}
(m) 

Calculation: Difference in potential energy U = M*g*(h_{1}h_{2})


acceleration due to gravity, g = 9.8 m/s^{2} 

Kinetic Energy Calculation 

Calculator Measurement: Final velocityv (m/s) 

Calculation: Final kinetic energy
KE = (1/2)*M*v^{2}


Trial #3 

Potential Energy Calculation 

Measurement: Mass of the cartM (kg)


Measurement: Original height (m) 

Measurement: Final height (m) 

Calculation: Difference in height h_{1}h_{2}
(m) 

Calculation: Difference in potential energy U = M*g*(h_{1}h_{2})


acceleration due to gravity, g = 9.8 m/s^{2} 

Kinetic Energy Calculation 

Calculator Measurement: Final velocityv (m/s) 

Calculation: Final kinetic energy
KE = (1/2)*M*v^{2}



Why aren't the potential and kinetic energy readings that we compare
exactly the same?

Pretend you were sliding down a snow hill on a sled with no friction,
just like the cart in the experiment. During your descent of the hill
describe how your gravitational potential energy, kinetic energy,
and total energy change.
 What would happen if we used a heavier cart in the experiment? Would
it have gone faster or slower, or the same speed? Why?

Assessment
Data sheet to be completed during the laboratory.
Students with special needs
Click here for information
on laboratories with students with special needs.
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