Download Experiment 10 – The Work-Kinetic Energy

Experiment 10 – The Work-Kinetic Energy Theorem
1
When investigating a physical system, it is often useful to determine the energies
involved. In this lab we will investigate how the work done on a system can change the
kinetic energy of that system. The Work-Kinetic Energy Theorem equates these two
quantities. First you will confirm this theorem for the case of “conservative” forces, then
you will use this theorem to determine the work done by a “non-conservative” force
(friction in this case). From this we will again determine the coefficient of kinetic
friction between a plastic-bottomed friction box and the dynamics track.
Materials
Science Workshop interface
Dynamics Track
Dynamics Cart
String
Stop Bracket
Bubble Level
Hanging and Bar Masses
Balance (500 grams +)
Photogate and Super Pulley
Plastic Bottom Friction Box
Screwdriver
1. Setting up the equipment.
1.1
Open data studio, create a new experiment
and connect the Smart Pulley and Force
Sensor to the science workshop interface.
1.2
Double click on the sensor window to bring
up the Force Sensor properties. Under the
“general” tab, make sure the sensor is set to
“slow force changes” (10 Hz).
1.3
Double click on the Smart Pulley Icon. Under the “measurement” tab select
position and velocity data.
1.4
Level the track both along and perpendicular to the direction of motion.
Note this is the single biggest step to ensuring success on this experiment.
1.5
Set up track, pulley and force sensor as shown by the instructor.
2. Calculating change in kinetic energy
2.1
Generate an equation for the kinetic energy of the cart-sensor system. You
will need to find the masses of the cart, force sensor, iron bars and hanging
masses you will use in this experiment. Under the Properties button, provide
a proper name and units for the Kinetic Energy. Ensure that the precision box
has the number three in it. Doing this sets the number of reported decimal
places to three.
2.2
Make a Kinetic Energy versus Position
graph. Make sure the position axes are
aligned. Producing a graph with
Experiment 10 – The Work-Kinetic Energy Theorem
2
position on the “x-axis” is a simple matter of dragging the position data onto
the “x-axis” of the graph you already have.
2.3
Your graph will look
similar to the one shown
to the right. The kinetic
energy will appear to
increase linearly with the
displacement.
2.4
This graph will make it
easy to confirm the work
kinetic energy theorem.
2.4.1 To find the change in
kinetic energy, you
will need to use the
“smart tool” (xy-tool).
Select a point at the
beginning of a straight-line portion of the graph using the tool and then
hover the cursor over one of the corners of the tool. You will notice a
small triangle appear near the cursor. Click and drag the cursor to the
other end of the data you wish to select. You should notice that both the
difference in position and Kinetic Energy appear parallel to their
respective axes (see graph above). Record both the change in kinetic
energy as well as the change in position.
2.4.2 To find the work done by the string on the cart you will need to do a
simple calculation. The force provided to the cart by the string will be
constant (the weight of the hanging masses). Because the force is
constant, the usual integral formula for calculating the work done by the
string is reduced to a simple multiplication. To calculate the work done by
this force, multiply the weight of the hanging masses by the change in the
position of the cart. This will give you a value in Joules.
2.4.3 If you have set up the graph correctly and taken accurate measurements of
the masses the Work and change in Kinetic Energy should be equal.
2.4.4 NOTE: Accurate mass values are crucial. A level track is a must. Be
sure to select only those data points for when there is an actual force being
applied to the cart. Data points once the hanging weight has hit the
ground are useless.
2.5
Perform this experiment using 2 different cart masses and three different
hanging masses for a total of 6 trials. A simplified version of your data table
is shown below.
2.6
Include a data table with your lab report. It should include all measured
and calculated quantities. An example is below:
Experiment 10 – The Work-Kinetic Energy Theorem
Work
Done by
Trial Mass Hanging Mass System String
Number
M1 (kg)
M2 (kg)
(J)
1
0.05
0.85
0.98
2
0.07
0.85
1.20
3
0.1
0.85
1.40
4
0.05
1.7
0.65
5
0.07
1.7
0.79
6
0.1
1.7
0.99
2.7
2.8
3
∆K2 (J)
% lost
0.93 5.10%
1.11 7.50%
1.32 5.71%
0.59 9.23%
0.76 3.80%
0.98 1.01%
Average Lost 4.66%
Print one graph with kinetic energy versus distance as shown in the
picture above during the course of these trials.
Find the percent difference between the work done by the string and the
change in kinetic energy of the cart in each measurement and decide if
there is another force present that you have not accounted for. Identify
this non-conservative force and find its average magnitude.
3. Friction
3.1
Now attach the string to the friction box and place 300 grams in the box.
Perform the same experiment you just did but note that because there is
another non-conservative force present. As a result, the work done by the
string and the change in kinetic energy will not be equal.
3.2
Knowing what your energy loss should be and the difference between
work and change in kinetic energy, calculate the work and then the
average force due to kinetic friction.
3.3
Calculate the normal force and estimate the coefficient of kinetic friction.
3.4
Print one Kinetic Energy versus Position graph during the course of these
friction-added trials.
3.5
Include all your measured and calculated quantities in a data table for
this experiment as well.
4. Lab report
4.1
Publish how you found the coefficient of friction for the plastic on
aluminum. Provide your data and how you estimated the percent of
energy lost in your system. Include your calculations and discuss how
someone else might go about confirming your data in another
experiment.