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ProCSI Hands-On Activity
Day 1: Engineering Measurement Lab
Introduction
Physics is defined as “the study of matter and energy and their interactions.” It is a set of
laws that describes everything around us and dictates how things interact. For example,
Newton’s 2nd law of motion is known as “the law of resultant force” and states that the
rate of change of momentum of a body is proportional to the resultant force acting on the
body and is in the same direction.
This definition probably doesn’t make a lot of sense and may be confusing so let’s break
it down and look at each part. Momentum, also known as inertia, equals mass times


p  mv
velocity
where ‘p’ is momentum, ‘m’ is mass, ‘v’ is velocity (speed) and
the arrows indicate that direction is important. When objects are sitting still they have no
momentum and when they are moving, they have a momentum of mass times velocity. A
Major League baseball weighs about 5 ounces, where the average bowling ball weighs
about 15 lbs. This means a bowling ball has about 48 times the momentum of a baseball
when they are moving at the same speed.
In order to change an object’s momentum (i.e., to stop the baseball’s movement) you
have to apply a force that counteracts the momentum of the object. To throw a baseball at
40 mph, a force is applied to the ball during the throw which gives it a certain amount of
momentum. To stop the ball, an equal and opposite force has to be exerted on the
baseball (minus the aerodynamic drag) to counter-act the momentum.
Figure 1: A baseball’s momentum is the product of mass times velocity
Mathematically, Newtons’ 2nd Law can be expressed as:
F  ma , where ‘F’ is the force (the arrow above means that direction is important),
‘m’ is the mass, and ‘a’ is the acceleration. If you caught a bowling ball with 48 times the
momentum in the same way that you caught the baseball (i.e., accelerate the ball to a stop
at the same rate), according to the equation it would take 48 times the force to do this!
Although you don’t have to be an engineer to know that playing baseball with a bowling
ball isn’t a great idea, engineers can solve a lot of interesting problems by knowing that
the laws of physics always apply and how they work mathematically. For example, if you
wanted to build a train that travels at 200 mph, how powerful does the engine have to be?
Can it travel on regular train tracks or do special track needs to be designed? How about
if you wanted to drop a 500 lbs. crate of food out of an airplane, how big does the
parachute have to be so that the crate doesn’t break when it hits the ground? An engineer
uses their knowledge of physics and math to overcome these types of challenges during
each and every design process.
Today, we will be testing the so called “laws” of physics. By setting up simple
experiments and taking measurements we can verify that important physical laws such as
Newton’s 2nd law are mathematically correct. We will start with a simple ‘system’ that
only has 1 force applied to it. This ‘system’ is a ball that drops due to the force of gravity.
We will use Newton’s 2nd Law and the Law of Gravitation to indirectly measure the
height of the 2nd and 3rd floor of the Mechanical Engineering Building, and prizes will be
awarded the groups whose measurements are the closest to the actual heights.
The second experiment is more complex, with up to 3 forces applied to the system at a
single time. This system is called a mass-spring-damper; variations of this type of system
are commonly found in our everyday lives.
Experiment 1: Newton’s Apple
Background
Some of you may be familiar with the story of Newton’s apple, where the famous
scientist Isaac Newton was inspired to investigate gravity when he observed an apple
falling from a tree. One version of the story says that he actually got hit in the head by the
falling apple, and the blow to the head inspired his work on gravitational theory.
Figure 2: Newton’s Apple
He would eventually write about universal gravitation in his famous manuscript “On the
motion of bodies in an orbit” (originally titled in Latin as De motu corporum in gyrum),
which explains how gravity affects the way planets and moons orbit each other.
Although Newton wasn’t the first person to investigate the idea of gravity (Galileo was
the first), it is the story of the falling apple that is the inspiration for the first lab. We will
use a ‘falling apple’ (a tennis ball in this case) to measure various heights.
Motivation
Use experimental measurements in conjunction with Newton’s 2nd law and the Law of
Gravity to calculate a desired quantity. Verify that the force of gravity is constant over
small vertical distances, and that Newton’s 2nd Law still applies after being extended
using math.
Procedure
Each team will be given a stopwatch and a tennis ball. To find the time required for the
ball to drop to the ground, start the stopwatch when the ball is dropped, and stop it when
the ball hits the ground. Repeat this experiment ten times and average the results to find
the average time required for the ball to drop to the ground. We will use this value with
the physical laws discussed earlier to derive the height of the 2nd floor railing. Repeat the
procedure to determine the height of the 3rd floor railing. For each height measurement,
the team that is closest to the actual height wins (one winner for each height
measurement).
Experiment 2: Mass-Spring-Damper System
Background
Mass-spring-damper systems are extremely common in engineering. From its title, there
are three types of force elements involved in the system: masses, springs, and dampers.
An engineering representation of this system can be seen below, where m is a mass, k is a
spring, and B is a damper. Figure 3 shows a ‘translational’ mass-spring-damper system,
where translational just means that it moves in a straight line. A few real life examples of
mass-spring-damper systems include: the suspension and tires of cars or trucks, muscles
and tendons in your body, and tuned mass dampers in tall buildings.
Figure 3: An engineering representation of a translational mass-spring-damper system
Figure 4: Taipei-101’s tuned mass damper (top), and its placement in the building
(bottom)
Motivation
Use a computer to do measurements on a complex system to verify that it obeys
Newton’s 2nd law just as simple systems do. Observe the free response of a single degree
of freedom mass-spring-damper system, and how its response changes as the mass is
varied. If time permits, extend lab to two degrees of freedom.
Procedure
We will be observing a mass-spring-damper system with “Position vs. Time” plots,
which are automatically created by the data acquisition software. Note that the plots
created during the activity have position units of ‘encoder counts’. These values can be
easily converted into an actual length value by using the conversion value in Table 1.
We will only be using the mass and spring on the rectilinear (translational) system with
the damper deactivated; a small amount of damping will be present due to friction. Some
of the plant specific information can be seen below in Table 1.
Spring Stiffness (k)
770 N/m
Mass of Weights (M)
0.59 kg (each)
Mass of Cart (Mc)
0.5 kg
Mass of Motor (Mm)
0.34 kg
Encoder conversion
2038 counts/cm
Table 1: System mass, stiffness and encoder values
Figure 5 below shows a rectilinear system similar to the one used in this activity.
Figure 5: A rectilinear system
Figure 6 shows a schematic representation of the system with only one mass carrier. The
system shown above in Figure 5 has three mass carriers.
Figure 6: Translational mass-spring-damper system used in this activity
The damping coefficient c in Figure 6 is unknown for these systems and must be
determined from experimental data. This will be done for you and details of the process
can be explained upon request (or try doing an internet search for “Logarithmic
decrement”).
The serial logger application should already be running on your group’s computer when
you begin the lab. See the instructor for assistance if this is not the case.
LabView Serial Logger Interface Settings
Baud Rate: 115200
Sample Rate: 250 Hz
Number of Samples: (Variable)
Position/Velocity Goal: 0
Read Variable 1 Name: Position
There are no write variables for this lab.
For each experiment, perform the following steps:
Inspect the Equipment
1. Inspect the system. Make a diagram of its components and note how the position
of the mass carrier is measured.
2. Observe how the system moves by displacing the mass carrier approximately 3
cm in either direction and releasing it.
3. Observe how the Position vs. Time plot depends on the starting position of the
mass carrier. Set the “Number of Samples” to a value which will record 10
seconds of data. Be sure that the “Save Data” button on the bottom is turned off.
First, press the “Run Experiment” button, then move the mass carrier 3 cm in
either direction and release it. Second, move the mass carrier 3cm in either
direction and hold it at that position. Have a teammate press the “Run
Experiment” button, and then release the mass carrier. Observe the differences.
Run the Experiment
Note: Be sure to press the “Run Experiment” button first, and then displace the mass
carrier to its starting position. This ensures that the position vs. time plots will settle at
zero.
1. We want to save our data for later use, so be sure the “Save Data” button is turned
on. Begin the first trial by making sure there are no masses on the mass carrier.
2. Press the “Run Experiment” button, displace the mass carrier 3 cm in either
direction, and then release it.
3. When the data acquisition software has logged the data, it will prompt you to save
the file. Give the data file a name that makes it easy to identify which experiment
it represents, and save it in the folder labeled “ProCSI” which can be found on the
desktop.
4. Add one mass block to the mass carrier, and run steps 2-3 again until there are
four mass blocks on the mass carrier.