Lab 9 - Conservation of energy
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Name: Katen Gulati, Chet BhattSection______________________
LAB: CONSERVATION OF ENERGY
Learning goals:
Choose a system appropriate to a given question and identify energy transformations and transfers for
a process.
Reason qualitatively and quantitatively with work, kinetic energy, gravitational potential energy, and
spring potential energy.
Reason qualitatively and quantitatively with power and efficiency.
Materials:
computer-based laboratory system
RealTime Physics Mechanics
experiment configuration files
force probe
old blue motion detector
screen to protect motion detector
large rubber ball (e.g., a basketball)
cart with adjustable friction pad
track
newer green motion detector
height adjustable ring stand
small ruler
If an object falls, then the potential energy becomes smaller and smaller as it falls toward the Earth while
the kinetic energy increases. We can think of kinetic and potential energy to be two different forms of
mechanical
energy. Is the mechanical energy constant during the time the object falls toward the Earth? If
it is, then the amount of mechanical energy doesn’t change, and we say that mechanical energy is
conserved.
The concept of mechanical energy conservation raises a number of questions. Does it hold quantitatively
for falling masses—Is the sum of the calculated potential and kinetic energies exactly the same number as
the mass falls? Often there are frictional forces involved with motion. Will mechanical energy be
conserved for objects experiencing frictional forces, like those encountered in sliding?
In this lab you will begin by exploring the common definition of
gravitational potential energy
to see if it
makes sense. You will then measure the
mechanical energy,
defined as the sum of gravitational potential
energy and kinetic energy, to see if it is conserved when the gravitational force is the only force acting.
You will explore what effects frictional forces have on systems – whether or not mechanical energy is still
conserved in such systems.
Investigation 1: Gravitational potential energy
1
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Suppose that an object of mass
m
is lifted slowly through a distance
y
. To cause the object to move upward
at a constant velocity, you will need to apply a constant force upward just equal to the downward
gravitational force.
Question 1-1:
Based on our energy equation from class, how much work will you do to lift the object
through a distance
y
? Explain.
W= Force x Distance
As distance increases, there will be more work done to the object. Furthermore, if there is less mass, the
force will be less which correlates to a smaller Work done on the object.
We define the gravitational potential energy
U
g
of an object of mass
m
to be equal to the work done
against the gravitational force to lift it:
U
g
=
mgy.
You’ll use this equation to calculate the potential energy of a ball.
Activity 1-1: Measuring Potential Energy
2
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1.
Use the blue motion detector on the floor with the screen on top of it.
2.
Open the experiment file called
Measuring Grav. Pot. E. (L12A1-1).
3.
Measure the mass of the ball: .0893kg
4. Examine the column entitled Gravitational Potential (
U
g
) calculated from mass times gravitational
acceleration,
g
times the position measured by the motion detector. Go under Data/Column Options/Grav.
pot. energy and enter the measured mass in place of the "1".
Display velocity on the top and kinetic
energy on the bottom, as shown on the axes that follow.
5.
Hold the ball from the sides or above with your hands. Starting with the ball about 0.5 m above the
motion detector (
keeping your hands and body out of the way of the motion detector
),
begin graphing
position and gravitational potential energy as you raise the ball to about 2.0 m above the motion detector.
Be sure that the ball remains directly above the motion detector.
6. Insert your graphs on the next page.
3
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Question 1-2:
Do the two graphs look similar? Does this surprise you? Explain.
Yes, the graphs both increase as I raised the ball up. This does not surprise me because as I raised
the ball, the position increased, and as you go higher, there is more gravitational potential energy
as you get to a higher value.
Question 1-3:
Gravitational potential energy is always measured with respect to a particular height
where its value is defined to be zero. In this case what has been chosen as this reference level? In other
words, for what location of the ball would its gravitational potential energy be zero?
If the ball was directly on top of the sensor, where it could not move downward anymore, then
there is no gravitational energy possible since it cannot fall anymore.
Question 1-4:
Suppose that the ball is dropped and you know its velocity at a certain time. What
equation would you use to calculate the kinetic energy of the ball?
K=1/2mv^2
Prediction 1-1:
Suppose that the ball is dropped from some height. What equation would you use to
calculate the mechanical energy (the sum of the gravitational potential energy and the kinetic energy)?
Mechanical Energy = Kinetic Energy + Gravitaitional Potential Energy
ME = K + Ug
Prediction 1-2:
As the ball falls, how will the kinetic energy change? How will the gravitational potential
energy change? How will the mechanical energy change?
As the ball falls, the kinetic energy will increase, and the gravitational potential energy will decrease. The
mechanical energy will stay the same.
Activity 1-2: Mechanical Energy
We can check the last predictions by measuring the two types of mechanical energy and their sum as the
ball falls.
1.
Open the experiment file called
Mech. Energy (L12A1-2)
to display the axes for
K, U
g
, and mechanical
energy vs. position that follow.
4
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2.
You will need to
enter
the mass of the ball (which you measured in the previous activity) into the
formulas in the software for kinetic energy and gravitational potential energy, so that these quantities
are calculated correctly. The mechanical energy is calculated as
U
g
+
K.
3.
Go to Experiment/Setup Sensors/LabPro 1 and click on the motion sensor and
uncheck
reverse
direction.
4.
You are now ready to examine how kinetic energy, gravitational potential energy and mechanical
energy vary as the ball drops. Hold the ball about 2 m directly above the motion detector.
Be sure that
it will fall on a straight path directly toward the motion detector.
5.
Begin graphing,
and
about 1-2 seconds soon after the motion detector starts clicking,
release the ball.
(The wait should keep you from recording multiple bounces.) (
Be sure that your body and hands are
out of the path of the motion detector after the ball is released.
5
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6.
Insert your graphs below and label the interval during which the ball was falling with arrows at the
beginning and end.
6
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Question 1-5:
How did the variation of kinetic energy and gravitational potential energy compare to
your predictions?
The gravitational potential energy decreased, and the kinetic energy increased as it got closer to
the sensor. This is the same as the prediction.
Question 1-6:
What seems to be true about the mechanical energy defined as the sum of the kinetic
energy and the gravitational potential energy? Did this agree with your prediction?
This is true, and the mechanical energy stayed constant, because as kinetic energy was increasing, the
gravitational energy was decreasing, which makes the mechanical energy stay constant throughout.
Another system where the gravitational force is essentially the only net force is a cart with very small
friction moving on an inclined ramp. You can easily investigate the mechanical energy for this system as
the cart rolls down the ramp.
Activity 1-3: Gravitational potential, kinetic, and mechanical energy of a cart moving on an
inclined ramp
1.
Set up the ramp and motion detector as shown below. The ramp should be inclined at an angle of
somewhere around 10°-15° above the horizontal. The friction pad on the cart should not be in contact
with the ramp.
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Question 1-7:
The gravitational potential energy of the cart which has traveled a distance
x
up the ramp
is
mgy,
where
y
is the height of the cart above the table top. You should be able to find an equation for
U
g
in
terms of the position
x
measured by the motion detector
along the ramp,
the length
L
of the ramp, and the
elevation
H
of the end of the ramp, using a bit of trig.
What is the reference height for the potential energy, i.e., the height where potential energy is zero?
When height = 0 or when it is on the table top, the gravitiational potential energy is zero.
2.
Measure the values of
L
and
H
. Also measure the mass of the cart. Write the equation for
U
g
from
Question 1-7 in the form of a single constant times
x
by using the values of
L
,
H
, (or for sin
) and the
gravitational acceleration, 9.80 m/s
2
.
L
: 1.21 m
H
: .28 m
m
: .54865 kg
U
g
= .54865 * .28 * 9.8 * sin(.28/1.21)= .006
8
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3.
Open the experiment file called
Inclined Ramp (L12A1-3)
to display the axes that follow.
4.
Enter
the mass of the cart into the formula for kinetic energy and the constant calculated above into
the formula for gravitational potential energy in the software.
Notice that mechanical energy is calculated as
U
g
+
K.
Prediction 1-3:
As the cart rolls down the ramp, how will the kinetic energy change? How will the
gravitational potential energy change? How will the mechanical energy change?
As the cart rolls down the ramp, the kinetic energy will increase. The gravitational potential energy will
decrease and the mechanical energy will stay the same.
5.
Be sure that the motion detector “sees” the cart all the way along the ramp.
6.
Hold the cart at the top of the ramp, and
begin graphing.
When you hear the clicks of the motion
detector, release the cart, and stop it when it is about 0.15 m away from the motion detector.
7.
Insert your graphs below.
9
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Question 1-
8:
Compare your graphs to those for the falling ball in Activity 1-2. How are they similar and how are they
different?
The gravitational energy decreases in both as it gets closer to the sensor, and the kinetic energy
increases as it gets closer to the sensor as well. However, the kinetic energy also increases slower
on the ramp since there is not full gravitational force acting on it. In the falling ball, there is a full
force gravity acting on the falling ball.
Question 1-9:
What kind of variation is there in the mechanical energy as the cart rolls down the ramp?
Does this agree with your prediction? Explain.
The law of conservation of mechanical energy is in use and it agrees with our prediction, this is because
the potential energy is being converted to kinetic energy and there is no energy lost to friction or air
resistance, meaning it is a closed loop and the energy is constant.
Prediction 1-4:
Suppose that the cart is given a push up the ramp and released. It moves up, reverses
direction, and comes back down again. How will the kinetic energy change? How will the gravitational
potential energy change? How will the mechanical energy change? Describe in words and sketch your
predictions with labeled dashed lines on the axes below.
10
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Test your predictions.
8.
Hold the cart at least 0.15 m away from the motion detector and
begin graphing.
(
Do not put your
hand between the cart and the motion detector.
) When you hear the clicks of the motion detector, give
the cart a push up the ramp. Stop the cart when it comes down again to about 0.15 m away from the
motion detector.
9.
Insert your graphs below.
11
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Question 1-10:
How does the
mechanical energy change as the cart rolls up and down the ramp? Does this agree with your prediction?
Explain.
Mechnical energy stays the same because of law of conservation of energy, the kinetic energy is turned
into gravitational consrvational energy which makes the value of mechanical energy the same.
Activity 1-4: Mechanical Energy and Friction
Prediction E1-5:
Suppose that there is also a frictional force acting on the cart in addition to the
gravitational force. Then as the cart rolls down the ramp, how will the kinetic energy change? How will
the gravitational potential energy change? How will the mechanical energy change? Compare your
predictions to the case you just examined where the friction was very small.
There will be less kinetic energy and gravitational energy will not be affected. This means that the law of
cosnservational mechanical energy will not be in effect since tehre are are outside factors acting on it.
This measn the mechanical energy will not be constant. Kinetic Energy is affected by friction since it
opposes motion, however gravitiational potential energy is not affected since it just depends on height.
Test your predictions. Is mechanical energy conserved when there is friction?
1.
Adjust the friction pad so that there is a significant amount of friction between the pad and the ramp,
but so that the cart still rolls down the ramp when released.
12
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2.
Using exactly the same setup as before, graph
K, U
g
, and mechanical energy as the cart rolls down the
ramp.
3.
Insert your graphs below.
13
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Question E1-11:
Is the mechanical energy conserved for the motion of the cart down the ramp
with
friction
?
No, the mechanical energy is not conserved since there is friction acting on it, the gravitational
potential energy is the same, but the kinetic energy is less. That means the gravitational potential
energy is at the a higher conversion rate to kinetic energy than the kinetic energy being produced.
Question E1-12:
If you found that the mechanical energy was not conserved as the cart rolled down the
ramp, explain what happened to the missing energy.
The missing energy is lost is converted to heat energy because of the friction being used. The energy has
to go somewhere and thermal energy that is created by the friction is the most possible outcome.
14
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