LAB 3: NEWTON’S SECOND LAW OF MOTION
Learning Objectives
1. Test the validity of Newton’s Second Law of Motion, F = ma, with both numerical and graphical
displays of the experimental results of measurements on a spinning mass system.
2. Learn the definitions and proper System Internationale (SI) measurement units for each of the
following physical quantities:
mass
inertia
time
velocity
force
distance
acceleration
3. Learn to differentiate between weight and mass, and between speed and velocity.
4. Learn to use the average of a number of small measurements in order estimate a single, small,
difficult measurement.
Background Scientific Principles
Newton’s Second Law of Motion predicts that a force acting on an object will cause that object
to move at ever faster and faster velocities. Velocity is similar in concept to the common idea of
speed. Speed is a measurement of how great a distance an object will move in a certain amount of
time. The term speed does not specify in which direction the object is moving. By contrast, the term
velocity not only specifies speed, but also specifies in which direction the object is moving. Velocity
is therefore a vector quantity, as explained in chapter 2 of your text, and speed is a scalar quantity. For
the purposes of this course, we will prefer the use of the term velocity, rather than speed. Velocity, V,
can be expressed mathematically as the distance, d, moved divided by the time, t, it takes to move that
distance:
V=d/t
When an object speeds up, or slows down, or changes direction, it is said to be undergoing
acceleration. The measurement of acceleration is how much the object’s velocity changes in a certain
period of time. Acceleration cannot be measured directly, but it can be calculated by measuring the
velocity, V1, waiting a measured period of time, then measuring the velocity again, V2. Acceleration, a,
is then calculated mathematically by dividing the difference between the two velocities by the time, t:
a = (V2 – V1) / t
In the case of an object moving in a circle at a constant speed, the speed itself does not change,
but the direction in which the object is moving is constantly changing. This means the object is
undergoing acceleration. Other experimental and mathematical work, the details of which need not
concern us, has established the relationship between acceleration, a, and velocity, V, in a circular
system with a circular radius of r:
a = V2 / r
Newton’s Laws of Motion assume that objects are free to move without any retarding forces of
friction to hold them in place or slow them down. Newton’s Second Law mathematically states that
the force, F, acting on an object is equal to the mass, m, of the object multipied by its acceleration, a.
F = ma
Force can be defined as any influence that tends to change the motion of an object, and can be
thought of as a push or a pull acting on an object. Mass is the measure of the inertia of an object.
Inertia or mass relates to how difficult it is to start a resting object into motion, or alternatively, once
the object is in motion, how difficult is it to bring it to a stop.
Distance is a measure of the amount of space between two objects or between two points.
Time is a measure of the passage of events.
The System Internationale (SI) is the measurement system used by common agreement
among the world’s scientists for measurement in scientific experiments. It is based on the European
Metric System. The Metric System and SI involve a system of decimal multiples and subdivisions of
the fundamental units defined by prefixes, described in chapter two of your textbook. The official SI
unit for measuring distance is the meter (m). The SI unit for measuring time is the second (sec), and
the unit for mass is the kilogram (kg). Force is measured in units called newtons. There is a useful
relationship between mass and the force of gravity that acts on a mass at the surface of the Earth, that
is used to define the newton. If allowed to fall freely, any mass at the earth’s surface is subject to a
constant acceleration, g, due to gravity, of g = 9.8 m / sec2:
F = ma = mg = m × (9.8 m / sec2)
This formula will give a value in units of kg m / sec2. Since these units are somewhat
clumsy to say, the newton has been defined as having the units of kg m / sec2.
The force acting on an object due to gravity is called weight. In common everyday useage, the
terms weight and mass are often used interchangeably, and the weight of an object is spoken of as
being measured in kilograms. It is only when we move away from the surface of the earth, or
accelerate at high rates that the gravitational field becomes so different that weight becomes different
from mass.
Materials
Hanging weights
Cork or rubber stopper
Nylon thread or fishing line
Hollow tube
Marking pen or pencil
Measuring Instruments
Laboratory balance
Meter stick
Stopwatch
Calculator
Experimental Procedure
1. Use the set-up illustrated below with a hollow tube, a string, a cork or rubber stopper, and a
hanging weight. During the procedure, record all data on the laboratory data sheet provided.
2. Using a laboratory balance, determine the mass of your hanging weight. Your instructor will
explain how to use the balance. Most laboratory balances determine mass in grams. If the
mass is printed on the weight, you may accept that value without measuring it. Your will
have to convert the mass in grams to kilograms by dividing by 1,000. Do not use the lightest
weight in your weight set.
3. Convert the mass in kilograms to a weight force in newtons, Fmeasured, by multiplying
by 9.8 m/sec2.
4. Using a laboratory balance, determine the mass m in kilograms of the cork or rubber stopper
that will serve as your rotating mass.
5. For the purposes of our experiment, we are going to ignore the mass of the nylon string.
Although theoretically it will affect our results, its mass is so small compared to the mass of
the hanging and rotating weights, that it will not appreciably affect our results by more than
a few per cent.
6. Tie the nylon string to the stopper stopper, thread the string through the tube, and tie a loop
in the end of the string on which you can hang the weight.
7. Mark or knot the nylon string just above the loop.
8. Draw the nylon string back through the tube until the stopper is stretched out in a straight
line from the upper end of the tube and the knot or mark is even with the lower end of the
tube.
9. Using a meter stick, determine the radius r, in meters, of the rotating stopper by measuring
the length of the nylon string from the upper end of the tube to the middle of the stopper.
10. Calculate the circumference C of the circle in which the stopper will travel, by multiplying
the radius r times 2. (C = 2r). This is the distance the stopper will travel in a single
revolution.
11. Hold on to the hanging weight with one hand and start rotating your hand until the stopper
spins out to the full length of the string. Adjust your rotating speed until the hanging weight
remains suspended, unsupported, with the knot or mark on the string right at the bottom of
the hollow tube.
12. Keeping the speed and radius constant by keeping the knot or mark at the bottom of the
tube, start the stopwatch and time the interval, in seconds, required for the stopper to revolve
twenty times. This is best timed by counting once each time the stopper passes a designated
point (e.g. the nose of the spinner or the stopwatch operator) near the outside of the spinning
circle. If you lose count, start over.
13. Divide the time for twenty revolutions by twenty to calculate the time t for one revolution.
14. To calculate the velocity of the stopper, divide the circumference of the circle by the time
of one revolution. (V = C / t).
15. To calculate the acceleration of the stopper, multiply the velocity by itself and divide
by the radius of the circle. (a = V2 / r).
16. To calculate the force Fcalculated, in newtons, on the stopper, multiply the mass of the
stopper times the acceleration. (F = ma).
17. Repeat this procedure three more times, using weights with a different value, until you have
four complete sets of data recorded.
Data Analysis
18. Prepare a summary force and acceleration table that shows the measured force,
Fmeasured, the calculated force, Fcalculated, and the acceleration a.
19. Using graph paper, prepare a single graph that plots two sets of points:
Fmeasured versus a
Fcalculated versus a.
The horizontal axis of your graph should be force, F, measured in newtons. The
vertical axis of your graph should be acceleration, a, measured in m / sec2.For each set of
four points, use a different plotting symbol, e.g. a circle for the first set (Fmeasured) and a square
for
the second set (Fcalculated). The title of your graph should be “Comparison of Acceleration vs.
Measured and Calculated Force in Newton’s Second Law.” Draw a legend below your
graph that shows which symbol represents Fmeasured and which symbol represents Fcalculated.
20. Draw two best fitting smooth curves, one through each set of points. If a straight line
seems to be the best curve, use a ruler or straight edge to draw it. If a curved line seems to
be the best curve, you can draw it freehand. Your instructor will draw a sample graph for
you, during class.
Questions
Answer the following 3 questions in your lab report.
In our experiment, the rotating mass (stopper) was always the same (a constant), and therefore
the formula F = ma represents a direct or directly proportional relationship. F is said to be directly
related or directly proportional to a. A graph of a direct relationship always looks like a straight line.
1. Do the graphs represent a direct relationship? Explain why or why not in the Results section
of your lab report.
If Newton’s formula for the second law, F = ma, is a correct statement, then measured
values of forces (Fmeasured) should be extremely close to the calculated values (Fcalculated).
Use both the graphs and the summary force and acceleration table to answer the following question.
2. Are Fmeasured and Fcalculated almost the same? Explain why or why not in the Discussion section
of your lab report..
Use your experimental data and your answers to questions 1 and 2 to answer the following, in
the Discussion section of your lab report:
3. Can you conclude that our hypothesis, that Newton’s Second Law is valid, has been verified
or falsified? Explain why or why not, using supporting data from your experiment.
RESERVED FOR NEWTON’S SECOND LAW DATA TABLE