Lab
LabPro: Newton's 2nd Law
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Purpose
The purpose of this lab is to let students become familiar with working with the Vernier LabPro and accelerated systems of bodies. Graphical data analysis, freebody diagrams and euqations dealing with Newton's 2nd Law will be used to calculate the mass of the rolling cart.
Equipment
meter stick
2 meters of string
rolling cart
slotted masses and calibrated hanger
LabPro attached to a computer station
motion detector
desktop pulley
triple beam balance
Procedure
Students will work in teams of two or three. On each team, one member will manipulate and measure the cart and suspended masses, a second member will operate the LabPro, and the third member will record the data provided in the group's data chart.
Connect the LabPro to the computer, clamp the pulley to the far end of the table, and place the motion detector on the table a minimum of 40 cm away from the cart's release position aimed at the back of the cart.
After measuring the mass of the rolling cart, securely tie one end of the string to its front axle. Pass the string over the pulley and tie the other end of the string onto the mass 50-gram hanger.
During the experiment you will add 50-gram increments to the hanger and release the cart. For each trial, track the cart's motion with the motion detector and record its acceleration in the chart provided below.
Under the Start Menu go to Programs, Math, Logger Pro 3.1 to launch the program.
Logger Pro should automatically set up the graphs according to the connected sensor. With the Motion Detector properly connected, the program should display graphs of position vs time and velocity vs time. First press Collect to start timing; then release the suspended mass.
With the completion of each trial, highlight the "smooth section" of your velocity vs time graph which displays the acceleration of the cart across the table. Then click on Analyze, Linear Fit, to obtain the slope of your line. Record your values to three significant figures in the chart provided. Repeat each mass increment two times until you have suspended a total of 400 grams.
One student MUST be available to "cushion the impact" of the suspended hanger and its masses just as they are about to impact with the floor. PLEASE do NOT allow them to crash on to the floor as we do not want to bend or damage the hanger or lose any slotted masses.
Data Table
Suspended
M
ass
(grams)
Trial 1
Trial 2
average
a
cceleration
50
100
150
200
250
300
350
400
Graph
Suspended
M
ass
(grams)
1/
M
(kg
^{-1}
)
1/
a
(sec
^{2}
/m)
50
100
150
200
250
300
350
400
Open the EXCEL graph PulleySystem.xls and chart your values. After filling in all required information, save your graph as
LastNameLastNamePulleySystems.xls
in your period folder. What was the filename of your graph?
What was the numerical value of the slope of your line?
What was the numerical value of the y-intercept of your line?
What was the mass of your cart using a triple beam balance?
Analysis
Step 1a
. On your graph's printout, draw a freebody diagram of the rolling cart (m). Include the forces tension, weight, and normal.
Step 1b
. On your graph's printout, draw a freebody diagram for the suspended mass (M). Include the forces tension and weight.
Step 2
. On your graph's printout, write the equations of motion for each body - the rolling cart and the falling suspended mass
Step 3
. We will now use data analysis techniques to determine the experimental values for the mass of the rolling cart and the acceleration due to gravity.
Initially solve these equations from Step 2 simultaneously for the suspended mass (M). Your solution should only involve letters - no numerical values.
Next rearrange this equation to match the format of the equation from your EXCEL graph where your y-axis variable is (1/a) and your x-axis variable is (1/M). Have your teacher check off your result.
Conclusions
Using the correct variables stated in Step 3 above, and EXCEL's values for your slope and intercept, state the equation of the line on your EXCEL graph.
By comparing your theoretical equation in Step 3 and the experimental equation from your EXCEL graph, what was your experimental acceleration due to gravity? Note: base this calculation solely on the graph's y-axis intercept not its slope.
What is your percent error for the acceleration due to gravity?
By comparing your theoretical equation in Step 3 and the experimental equation from your EXCEL graph, what was the experimental mass of your rolling cart? Note: base this calculation on your graph's values for both its slope and y-intercept.
What is your percent error on the mass of the cart?
Did the acceleration of your trials increase uniformly? That is, with the addition of each 50 grams of mass to the hanger, did the system's acceleration increase by an equally consistent amount? Support your answer.
After submitting your online results, your written lab report should include a cover sheet along with a printout of your EXCEL graph with your freebody diagrams, the calculations for the mass of the rolling cart and its percent error as well as the calculations for your experimental value for the acceleration due to gravity and its percent error.
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