Download Newton`s Second Law

Physics Lab
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Dynamics of Motion: Newton's Second Law
Introduction
The goal of this experiment is to investigate the relationship between force, mass and
acceleration. You will be verifying a powerful physical law well known as Newton's
second law. F = ma You will also be comparing the gravitational mass of an object
with its inertial mass. Where: m=W/g (gravitational) should equal m=F/a (inertial)
In order to investigate the relationship between force and acceleration in Newton’s
Second Law, you need to experimentally obtain force and acceleration data. The
directions below will enable you to setup an experiment where you will apply a constant
force on a mass and measure the value of the resulting acceleration. You will be able to
make (8) trials continually increasing the force and measure the acceleration, while
keeping the mass constant. At the completion of data acquisition, you will
construct a graph of Force (y axis) versus acceleration (x axis) to analyze the
relationship between force and acceleration and determine the inertial mass.
The following directions will teach you how to use the computer to determine the
acceleration of a system of mass experiencing a constant force.
Setup the track and balance by adjusting the all threads at the end of the track. Attach
the smart pulley at the end of the table, near the computer. Tie the pulley cord to the
cart and run the weight over the pulley. The weight holder should be attached so it is
near the top of the pulley. The goal is to let the weight holder fall under the influence of
gravity while applying a constant force to the glider. The amount of weight falling is
the F in F = ma.
Open the Logger pro program. Open the experiment file menu. Load experiment 10,
Atwood’s Machine. This will load the smart pulley interface program that will enable you
to make a velocity time graph of the motion of the cart.
This section teaches you how to determine the acceleration of a system of
weights.
To test Newton’s Law, you will vary the accelerating force while keeping the total mass
of the system constant. This is done by carrying small masses in the slot on top of the
glider, and selectively transferring mass from glider to weight holder. Obtain 4 (20) gram
masses and a 10 gm mass from the weight set. Make a trial run by letting the glider
accelerate under the influence of the weight holder with a 20 gram mass (0.025 kg
total) and place the remain masses in the slot in the cart. You do this to keep the total
mass of the system constant. Later to increase the amount of force acting, take mass
from the cart and place it on the mass holder. Have another person start the timing by
selecting collect button. Wait a short time before letting go of the glider. Stop the cart
before it crashes into the end of the track. Pressing stop stops the timing. The graph
appears in almost real time.
To fit the data on the screen, select the Autoscale feature (A) on the menu bar. This will
give you a line with the beginning being linear and a “rough” line after the weight hit the
ground. Highlight the linear portion of the graph and select the regression button to find
the slope of the line (rx).
Remember you are doing all of this to find the slope of the v vs t graph.
You should increase the mass in 10 gram increments. Remember the weight holder's
mass is 5 grams! You have enough masses to make eight trials. Record the
acceleration in the data table after each run. Remember, at the completion of the
lab you will have constructed a graph using the Graphical Analysis program to
determine the relation ship between force and acceleration, the value of the
inertial mass.
Make sure you remember to find the mass of the entire system of masses. That is
the glider and additional masses!
Confirming Newton’s Second Law.
Open Graphical analysis. Force is to be plotted on the y axis and acceleration on the x
axis. After plotting your data pairs, remember to remove the line connecting the points.
Fit the data points accordingly.
Question
1. Describe the mathematical relationship between force and acceleration.
2. Write down the equation of the line with the appropriate variables.
Determining the inertial mass
3. What quantity in F= ma does the slope of the line of your graph represent?
Remember slope equals the y value / the x value. What unit of measure is the slope
quantity measured in?
4. Record the value of the slope with the associated units of measure.
5. What was the value of the mass of the entire system being accelerated? What was
the value of the slope of the line? Record these values below. Determine the percent
error found in the measured mass and the experimental (inertial mass) using the
measured mass as the accepted value.
Gravitational Mass = (from the scale) ________________
Inertial Mass = (from your graph) ____________________
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6. Calculate the value of the ideal acceleration (with out friction) of the system when
using the 55 grams mass as the force causing the acceleration and the measured total
mass being accelerated (cart and masses).
7. Compare the calculated acceleration with the measured acceleration with the 55
gram mass acting. Determine the difference between these values.
8. Using F = ma, determine the approximate value of the force of friction using the mass
of the cart and masses and the difference in acceleration from above.
9. Error analysis. When there is a discrepancy in a result, experimenters have to
consider conditions in the experiment out of there control. They describe how these
conditions affect the “intended “ outcome. In this experiment, the value of inertial mass
and gravitational is not equal, though very close. That is gravitational mass does not
exactly equal inertial mass. This is important in verifying F= ma! How can the same
measurement not be equal and this be a fundamental law of nature?
(Remember: m=W/g (gravitational) should equal m=F/a (inertial)
In consideration of the experimental procedure, explain why these values are not exactly
equal; which value is “greater” and why.
10. How would the inertial mass compare to the gravitational mass if friction was
eliminated from the experiment?
Your lab report will include:
Statement of the problem
Data
Graph
Answers to questions
Conclusion: Describe the relationship between force and acceleration in
Newton’s second law as tested in this lab, and compare inertial and gravitational
mass.
Error analysis: Why are the mass values different?
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Data Table
Combined mass of system = __________________Kg
(carts + Masses = system)
Mass on holder
(kg)
weight causing acceleration
(Newtons)
0.05 kg x 9.8 m/s/s =
50 g = 0.05 kg
0.49 N
55 g
60 g
65 g
70 g
75 g
80 g
85 g
90 g
95 g
100 g
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acceleration
(m/s/s)
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