Physics 211:
Newton’s Second Law
Sir Isaac Newton
Born: January 4, 1643
Died: March 31, 1727
Reading Assignment:
Chapter 5, Sections 5-9
Chapter 6, Section 2-3
Portrait of Isaac Newton by Sir Godfrey Kneller
http://www.newton.cam.ac.uk/art/portrait.html
Introduction:
Kinematics is the study of how objects move. Dynamics, on the other hand, focuses upon
why objects move. Our own human experience tells us that forces have something to do
with causing motion. Aristotle developed a theory of motion based completely upon
human experience and reason. He stated simply that all motion, even constant velocity,
was caused by the existence of forces. Objects at rest, according to Aristotle, had no
forces acting upon them. Spontaneous motion, such as letting go of a rock and watching
it magically pick up speed as it fell to the earth, was explained by the fact that all objects
had a natural place in the universe. A rock’s natural place was on the ground. Therefore,
when a person released a rock from their grasp, it automatically returned to its natural
place. The force arose from the object being out of its’ “natural” place and wanting to
return to its “natural” place. Aristotle, however, never actually verified his theory with
experimentation. If he had, he would have found flaws in his thinking.
Many people today still hold Aristotelian views. However, Newtonian theory takes a
very different stance. The power of Newton’s theories was revealed through their ability
to make detailed mathematical predictions about the motion of objects. These predictions
have consistently been verified experimentally. Newton hypothesized that forces cause a
change in motion, not motion itself. In addition, he carefully distinguished between
individual forces and the net force acting on an object. He said that if the Net Force
acting on an object was zero, then the object would continue to move with constant
velocity. Constant velocity includes two important parts: constant magnitude (speed) and
constant direction. [Note: 1) An object at rest is a special case of the speed being equal to
zero; 2) A frame of reference is needed to define each of these parts.] In a sense, Newton
felt that moving at constant velocity was an object’s “natural place in the universe.”
Newton also carefully explained what would happen to an object that experienced a Net
Force with a magnitude of something other than zero.
Fnet  ma
© 2004 Penn State University
Physics 211R: Lab – Newton’s Second Law
This version of Newton’s Second Law is popular because it clearly demonstrates the
relationship between Net Force and Acceleration.
After studying kinematics,
acceleration is a quantity with which many students are familiar and comfortable.
Similarly, most people are familiar with the concept of Force, but many do not have a
realistic number sense of its magnitude expressed in newtons. For example, what is the
magnitude of the force provided by a Saturn V rocket (i.e. Thrust)? How does the force
on a basketball differ from the force on a bullet when each is “shot?” Many people are
not aware that a bullet and a basketball each experience approximately the same change
in momentum. Why would this be? As you perform this lab, make some mental notes
regarding the size of the values that you calculate for your answers. It is essential that
you develop a good sense of what is realistic.
© 2004 Penn State University
Physics 211R: Lab – Newton’s Second Law
Newton’s Second Law
Goals:


Verify that a constant net force causes a constant acceleration by collecting data,
graphing each vs. time, and analyzing the data during the appropriate time
interval.
Determine the mass of an unknown object by graphing Net Force vs.
Acceleration.
Equipment List:
Low Friction Track with cart
Ultrasonic motion detector
force probe
pulley system
Science Workshop
Excel™
scale balance
hanging masses
灺
Shown at left is NASA’s Saturn V rocket as
it blasts off on July 16th, 1969 with the crew
of Apollo 11 sitting on top. The Saturn V
rocket was the largest rocket ever used by
NASA, and the only one able to lift the large
masses needed to land astronauts on the
moon.
Photo courtesy of NASA
Lab Activity 1: Determine the Mass of an Unknown Cart
What is the mass of the cart (including the force probe) sitting on the track at your lab
station? One way to measure mass is to use a scale balance. However, this method will
not be available to you until the end of the lab. Therefore, you must find it indirectly
using another method. Newton’s 2nd Law states: “if a net force acts upon an object, then
the object will respond by accelerating in the direction of the net force.” In addition, a
constant net force should result in a constant acceleration.
Fnet  ma
© 2004 Penn State University
Physics 211R: Lab – Newton’s Second Law
This method uses the motion detector and force probe to measure the acceleration and net
force, respectively, acting on the cart. The net force is caused by a mass that is hanging
over a pulley at the edge of the track. Gravity ensures that this force will be constant.
Once this data is taken, the mass can easily be calculated.
It is important to note, however, that all good experiments rely upon more than one data
point. Therefore, you will repeat this experiment for different accelerations and
corresponding net forces while keeping the mass (the cart) the same. All of the data will
be graphed together to determine the mass.
1. Set up Science Workshop to read the data
collected by the motion detector and force
probe. Create graph windows of Position,
Velocity, Acceleration, and (Net) Force vs.
Time so that the data will be displayed on
the screen as each run is taken. The motion
detector does not need to be calibrated.
However, the force sensor must be rezeroed often throughout the lab. In order
to do this, first remove all tension from the
force sensor. Then, press the TARE
button to reset the force sensor to zero1.
Repeat this procedure before each trial.
2. Place a hanging mass at the end of the
string.
(Suggestion: 20g, 40g, 60g, …)
3. Release the mass and record your data.
4. Using the graphs that you created on
Science Workshop, notice the time interval
during which the cart was being freely
pulled by the hanging mass. (The force and acceleration data should be relatively
constant.) Click and drag to highlight this region on each graph. (Note: the graphs
can be resized and enlarged.)
5. Using the  icon on Science Workshop, perform statistics calculations on this region
of the data for this trial. Calculate:
(1) the Acceleration and
(2) the Net Force.
Hint#1: the constant net force is the mean y-value of this region of data on the
force vs. time graph.
1
Calibration of the Force Probe
See the previous lab (Newton’s First Law) for instructions on how to calibrate the force sensors.
© 2004 Penn State University
Physics 211R: Lab – Newton’s Second Law
Hint#2: the constant acceleration is either the mean y-value of this region of data
on the acceleration vs. time graph or the slope of this region of data on
the velocity vs. time graph.
6. Open Excel™. Create a table in which to place the Acceleration and Net Force data
point that you determined in step 5. Place these values in your table as one data
point.
7. Repeat steps 2-6 for at least 6 different hanging masses. (Note: This will provide a
set of 6 data points from which the mass can be determined.) Import the Excel™
Acceleration and Net Force Table containing all of your collected data into the
Template.
8. Construct a Net Force vs. Acceleration graph in Excel™. (Import this graph into the
Template.) What does the slope of this graph represent? Find the value of the slope
(including units). Does your graph pass through the origin? If not, explain why it
doesn't.
9. Measure the actual mass of the cart (including the force probe) using the scale
provided by your TA.
10. Calculate the % error between the calculated and actual values for the mass of your
cart. (By what percentage does your calculated mass differ from the mass measured
on the scale?) Comment on the result by including a discussion of error in your
answer. (Hint: You may wish to complete Activity 2 before completing this question.)
Lab Activity 2: Free Body Diagrams
1. Draw a force diagram of the cart as it is being pulled across the level track. If the
Net Force does not equal zero, then also indicate the direction of the Net Force on
the cart.
2. Draw a force diagram of the hanging mass as it is allowed to fall freely, pulling
the cart. If the Net Force does not equal zero, then also indicate the direction of
the Net Force acting on the hanging mass.
3. What force does the force probe actually measure? (In Activity 1, it is stated at
measuring the Net Force. Is this true? Under what conditions?)
4. Compare the value of the Net Force (measured by the force probe) in each of your
6 trials in Activity 1 to the actual weight of the hanging mass. Are they equal? If
not, which one is greater and why?
© 2004 Penn State University
Physics 211R: Lab – Newton’s Second Law