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Name _____________________________ Section (Period) _________________ Date __________________
Lab Partner(s) _____________________________________________________________________________
P A P E R R O L L E R C O A S T E R L A B
Calculating Potential Energy and Kinetic Energy of
a Rolling Marble
INTRODUCTION AND OBJECTIVES
The Law of Conservation of Energy states that energy can be
neither created nor destroyed. However, energy can change from
one form to another. In the case of a marble on a paper roller
coaster, a marble starts at the top of the roller coaster with a
relatively large amount of potential energy and no kinetic energy.
As the marble starts rolling down the roller coaster, the amount of
potential energy stored in the marble decreases while its kinetic
energy increases. Potential energy is also converted into heat
energy due to friction. In this experiment, you will be calculating
the change in potential energy of a marble traveling between two
points on a paper roller coaster and compare that to the kinetic
energy that was gained by the marble during that same time.
EQUIPMENT NEEDED
completed Paper Roller Coaster
ruler
pencil
calculator
•
•
•
•
stopwatch (optional)
video camera (optional)
photogate timer (optional)
•
•
•
PROCEDURE
I. Selecting the starting and ending points.
Choose a portion of the roller coaster in which the
marble accelerates and then keeps a fairly constant
speed. Ideally, this would mean a gentle downhill sec-
tion followed by a level section. The marble does not
need a steep hill to accelerate.
Place three marks on the roller coaster. Label the be-
ginning of the hill “A”, the end of the hill “B”, and the
end of the level section “C”. You will be measuring
the distance between each of these points so make sure
that those distances will be easy to measure.
II. The gravitational potential energy of the marble
To simplify calculations, treat the height of point
B as the reference point where gravitational poten-
tial energy equals zero. The gravitational potential
energy of the marble depends on the height of the
Find the mass of the marble. Measure the mass of ten marbles and divide that by ten. Convert the mass of the
marble to kilograms. Enter your result below.
Find point A’s height above point B in meters.
1. Mass of the marble, m (kg)
2. Acceleration due to gravity, g (m/s
2
)
3. Height of point A above point B, h (m)
4. Gravitational potential energy at point A, mgh, (J)
starting point compared to the ending point of the
marble’s path. Gravitational potential energy equals
(mass)*(acceleration due to gravity)*(height). This
can be written as P.E.= mgh.
©2012 Paper Roller Coaster Company
A
A
B
C
h
III. Calculating the kinetic energy of the marble
The total kinetic energy of the marble is made of two
parts, the kinetic energy due to its linear motion and
the kinetic energy due to its rotation. A marble that
is rolling has more kinetic energy than a marble that
is sliding along at the same speed. You will calculate
those two amounts separately before adding them
together.
A. Kinetic energy of the linear motion
The marble’s kinetic energy due to the its linear motion is one half its mass times its velocity squared. It can be
written as K.E.
l
=
1
/
2
mv
2
.
1. Find the mass of the marble. Enter all results below.
2. Find the velocity of the marble between points B and C. There are many ways to do this. The simplest way
(although the least precise) is to use a stopwatch to determine how long it takes to get from point B to point C
after you release the marble at point A. Divide the distance between points B and C by the time elapsed. Con-
duct three trials to determine the average velocity between points B and C.*
3. Calculate the average linear kinetic energy of the marble.
Trial #
Linear Distance
from B to C (m)
Time (s)
1
2
3
Average
B. Kinetic energy due to rotation (optional)
The marble’s kinetic energy due to its rotational speed
is 1/2Iω
2
, where I is the moment of inertia of the mar-
ble and ω is the marble’s angular speed. The moment
of inertia of a solid sphere is
2
/
5
mr
2
, where m is the
mass and r is the radius of the marble, so the kinetic
energy of a rotating marble is K.E.
r
=
1
/
2
(
2
/
5
mr
2
)ω
2
.
For a marble that is rolling without slipping, ω=v/r,
*For more precise measurement of the marble’s velocity, use either a photogate timer or a video camera. A video camera can be used
if it allows for frame by frame advance and an on-screen display showing elapsed fractions of a second.
C. Total kinetic energy of the rolling marble
The marble’s total kinetic energy is the sum of its linear kinetic energy and its rotational kinetic energy.
Total kinetic energy of the rolling marble = ___________________ (Kg)(m
2
)/s
2
= Joules.
P A P E R R O L L E R C O A S T E R L A B
©2012 Paper Roller Coaster Company
so K.E.
r
=
1
/
2
(
2
/
5
mr
2
)(v/r)
2
, or
K.E.
r
=
1
/
5
mv
2
.
Mass of marble (Kg)
Velocity of marble (m/s)
Rotational Kinetic Energy
(J) K.E.
r
=
1
/
5
mv
2
IV. Conclusion
1. What is the total Mechanical Energy of the marble at point A, before the marble starts to roll? ____________
2. What is the total Mechanical Energy of the marble at point C? _____________________________________
3. Compare your answers to questions 1 and 2. Should these answers be the same? _______________________
why or why not? ____________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Average Velocity (m/s)
Mass (Kg)
Linear Kinetic Energy (J)
K.E.
l
=
1
/
2
mv
2
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Completed 27 June 2022

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