
 University of Virginia
 Physics Department

Change in Energy of a Cart on a Ramp (Version
A)
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 TI made 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 CBL calculator system to calculate instantaneous velocities;
 use the following skills: observing, comparing, inferring, predicting,
experimenting with variables, and plotting graphs of variables.
For instructions on how to download the CBL programs necessary for this activity,
click here.
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 with 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
CBL. 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 CBL with motion
detector 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 lose 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 calculator (TI83 or 83 plus preferred, but TI82 is
okay)
 Texas Instruments CBL unit
 Vernier motion detector
 The PHYSICS suite of programs from Vernier.
 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 CBL unit to the TI Calculator with the unittounit link cable
using the I/O Ports located on the bottom edge of the units. Connect the motion
detector to the CBL by the SONIC port on the side of the CBL.
 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 know to determine the potential
energy.
 Start the PHYSICS program on the TI calculator.
 In the main menu, select 1. SET UP PROBES and follow the prompts for
ONE Probe and MOTION Probe, and then return to the main menu.
 In the Main Menu select 2. COLLECT DATA.
 In the Data Collection Menu select 2. TIME GRAPH.
 Enter in the following values: Enter Time Between Samples in Seconds:
.05 Enter Number of Samples: 50 Then the calculator will determine how
much time the experiment will take. With these values it will take .05
* 50 = 2.5 seconds. You may have to change these values for your particular
set up.
 Then select 1. USE TIME SETUP. The device is now ready to collect data.
 Hit the Enter button and release the cart. The motion detector will measure
the position and velocity of the falling cart. Wait until the calculator is
finished with its measurements.
 In the Select Graph menu, choose 2.VELOCITY, and a graph similar to the
one below will show up. It shows the instantaneous velocity in the yaxis
for a given time in the xaxis.
 The graph will have some spikes in the beginning which represent the time
when the cart was let go. These can be ignored. The most important part of
the graph is the peak that represents the final velocity right before the
cart hits the sponge. The graph is already in the TRACE mode so by using the
left and right arrows, place the cursor at the final peak velocity value and
read off the y value at the bottom of the screen. The units are m/s. The x
value represents the time in seconds.
 Calculate kinetic energy ( ½ mv^{2}) and potential
energy loss {m*g*(h_{1}h_{2})}
and compare results. Perform this calculation for varying heights of the ramp.
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.