Download Newton`s Second Law - Dallastown Area School District Moodle

Newton’s Second Law
OBJECTIVE: To determine how an object’s acceleration is dependent upon its mass
and the net force acting upon it.
INTRODUCTION:
Sir Isaac Newton was one of the greatest minds of all time. His contributions to
science span a wide range of subjects, including mechanics, astronomy, gravitation,
optics, and even calculus (which he invented in order to solve certain problems in
physics). It was his study of the forces surrounding us which has become the basis for
what has come to be called classical mechanics. Newton’s three laws of motion are still
taught today, hundreds of years after his death. His second law in particular is
mathematical in nature and allows us to predict the motion of a body after some force has
been applied to it.
METHOD:
An air track will be used to reduce friction, allowing the cart on it to slide freely.
The cart will be made to accelerate by attaching it to a pulley and weight system, as
shown below. The mass of the cart and weight system can be easily measured (the total
mass of the system must be considered), and the force acting on the system is simply the
weight attached to the pulley.
The computer and two interfaced photogates will be used to determine the
acceleration of the cart as it moves along the track. The computer will measure the time
required for the cart to pass through each photogate as well as the time interval from
when the cart last exits the first gate until it first enters the second gate. However, to find
the cart’s acceleration, we need the time interval between the average velocities (vf and
vi) measured at the two gates (in other words, the time interval from when the middle of
the cart exits the first gate and enters the second). The cart’s acceleration may then be
v f  vi
found using the equation a 
, where t may be found by adding the measured time
t
interval to one half of the time taken to pass through the first gate plus one half of the
time taken to pass through the second gate:
t  t measured 
1
1
t first gate  tsec ond gate
2
2
You will use Logger Pro 3.x to measure the time for the cart to pass through the
first gate, the time for the cart to pass through the second gate, and the time between the
two gates. You will then create and use an Excel spreadsheet to calculate the corrected
time between the two gates, the cart’s velocity at each gate, and the cart’s acceleration.
This experiment will consist of two parts. In the first part, you will vary the
system’s mass and measure its acceleration while the force acting on it is held constant.
In the second part, you will vary the force acting on the system and measure its
acceleration while its mass is held constant.
DATA TREATMENT:






Hanging weight
Velocity of cart
Corrected time between gates
Acceleration of cart
Include any additional calculations required to answer specific
interpretations/analysis of errors questions with the answers to those questions
Be sure to include all three graphs, labeled as to which is for Part I (constant
force) and which is for Part II (constant mass).
DATA:
Constant Force
Hanging Mass: _____________ kg
Hanging Weight: _______________ N
Length of Cart: _____________ m
Trial
Mass of Empty
Cart (kg)
Mass Added to
Cart (kg)
Hanging Mass (kg)
Total System Mass
(kg)
1
2
3
4
5
6
Trial
1
2
3
4
5
6
Time
Through
Gate 1 (s)
Time
Through
Gate 2 (s)
Measured
Time
Between
Gates (s)
Corrected
Time
Between
Gates (s)
Gate 1
Velocity
(m/s)
Gate 2
Velocity
(m/s)
Acceleration
(m/s2)
Constant Mass
Mass of System: ________________ kg
Trial
Hanging Mass (kg)
Force Acting on
System (N)
1
2
3
4
5
6
Trial
1
2
3
4
5
6
Time
Through
Gate 1 (s)
Time
Through
Gate 2 (s)
Measured
Time
Between
Gates (s)
Corrected
Time
Between
Gates (s)
Gate 1
Velocity
(m/s)
Gate 2
Velocity
(m/s)
Acceleration
(m/s2)
INTERPRETATIONS:
1. Plot a graph of acceleration versus total system mass for your constant force data
(Part I). Based on your graph, what kind of relationship exists between a system’s
acceleration and its mass when the force is held constant?
2. Test your conclusion to #1 by plotting a different graph, to yield a straight line.
What is the slope of this line? How can the force acting on the system be found
from this value? Explain your reasoning.
3. Plot a graph of acceleration versus force for your constant mass data (Part II).
Based on your graph, what kind of relationship exists between the acceleration of
the system and the net force acting on it when its mass is held constant?
4. What is the slope of your straight line for #3? How can the mass of the system be
found from this value? Explain your reasoning.
ANALYSIS OF ERRORS:
1. Calculate the % error between the force obtained from the slope in interpretation
question #2 and the actual constant force used in every trial of part I.
2. Calculate the % error between the mass obtained from the slope in interpretation
question #4 and the actual constant mass used in every trial of part II.
3. How would the friction between the air track and cart affect your results in this
experiment (would the measured accelerations be lower or higher than predicted)?
4. If you knew the value of the frictional force between the cart and track, how
would you use it to find the corrected net force acting on the cart?
5. Discuss some sources of error in this experiment.
Physics Computer Lab. Software Guide
Using the Photogates to Measure Acceleration
1. Navigate to the honors physics shared files folder (from either the school web site
physics page or the Honors Physics I moodle page). Open the “Class Materials,”
“LoggerPro” folders. Click on the file “Acceleration” and open the file. Click on
“Connect” to connect to the interface.
2. Make sure that your first photogate is plugged into “DIG/SONIC 1” and your
second photogate into “DIG/SONIC 2”¨ on the LabPro interface that is connected
to your computer.
3. Make sure that the cart is ready to release and clear of both photogates. Then
click on the “Collect”
button at the top, right of the toolbar.
4. Release the cart. Be sure to stop it before it rebounds and passes back through the
gates.
5. Click on “Stop” when you are finished.
6. Repeat steps 4-6 for as many trials as you need to do.
7. When you are completely finished, select “Exit” from the “File” menu (do not
save your changes.)
Physics Computer Lab. Software Guide
Using Excel to Calculate Acceleration
1. Navigate to the honors physics shared files folder (from either the school web site
physics page or the Honors Physics I moodle page). Open the “Class Materials,”
“LoggerPro” folders. Click on the file “Acceleration Excel” and open the file.
2. Click on the “Edit Workbook” tab and choose “Edit in Excel.”
3. Enter your time data into the first three columns of the data table.
4. Click on the first empty cell of the “Corrected Time” column (cell D3). You will
now enter the formula for the computer to calculate the corrected time between
the gates. To do this, enter an “=”sign in the formula window. Enter the formula
to the right of this sign, and press enter when finished. To enter the contents of
cell A3, for instance, you may either click on cell A3 or type “A3.” Either way,
“A3” will appear in the formula window. For example, to calculate half of the
gate 1 time, “=A3/2” should appear in the formula window.
5. After you have checked the value displayed in cell D3 and are satisfied that it is
correct, you will copy the formula to the rest of the cells in column D. To do this,
place the cursor on the small square at the lower right corner of the cell
(cursor will change to a small “+” sign). Click on the square and drag the cursor
over all of the remaining data cells in column D.
6. Click on the first empty cell of the “Velocity 1” column (cell E3). You will now
enter the formula for the computer to calculate the cart’s velocity at gate 1. Do
this using the procedure in step 4 above. Note that you will need to enter the
length of your cart, in meters, in the formula. When you are satisfied that the
velocity has been correctly calculated, copy the formula into the other cells of
column E using the procedure from step 5 above.
7. Repeat step 6 to calculate the remaining values in the table.
8. When you are completely finished, close Excel. Do not save your changes to the
file.