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National Science Foundation
Project Summary
Development of Job-Based problem Sets for Technical Physics
Job-based problems similar to those technology students are likely to
encounter when they begin work in industrial settings are not widely available
for technical physics courses. Consequently, students frequently fail to see
the relevance of physics to their studies and may not recognize physics-based
applications when they encounter them on the job. The objective of this project
is to develop 120 job based problems for technical physics. These problems will
be jointly developed by physics and technology instructors, representative from
the
PROBLEM 1
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Overview of the Steel Making Process at US Steel Fairfield, Alabama.
In steel fabrication plants a device called a finishing stand has rollers that compresses steel slabs. In one plant six finishing stands are in a row and compress 1 inch thick steel slabs to 0.1 inch thick pieces. This process does not change the density or width of the slab, but change its length. The density of steel is 7.8 x 1000 kg/m3. The density of copper is 8.9 x 1000 kg/m3. A work order was received to make a 4000 ft. piece of steel slab 42" wide and 0.1" thick.
(a) The measurements in this problem are standard for this industry so they are in English units. Convert each measurement in the diagram to metric.
(b) If the slab is 42" wide, what length of 1" thick slab will be needed?
(c) Find the total mass of steel used in this process.
(d) What would be the total mass if copper is used instead of steel?
(e) What is the average acceleration of a point on the slab between A and B, a distance of 100 feet?
(f) How long does it take for the process in part (e) to be completed?
PROBLEM 2
In
the steel industry there is a need to carry large slabs of steel from one place
to another. This is accomplished by use of the Kress Carrier. The Kress Carrier
is a large straddle carrier that is capable of handling up to 100 tons of steel
slabs at a time. The carrier drives over (straddles) the slabs, and its
hydraulic tongs lift the slabs. There are two tongs.
- If the mass distribution of slabs is uniform, find the maximum force that each tongue must apply in order to hold 100 tons of slab.
- How much additional force must be applied by the Kress Carrier in order to overcome the inertia of a 100 ton slab. The carrier accelerates at 2 m/sec/sec.
2a. In the steel industry there is a need to carry large slabs of steel from one place to another. This is accomplished by use of the Kress Carrier. Find the work done on the slab if the Kress Carrier moves a 100 ton slab on a flat road for a distance of 200 m.
PROBLEM 3
In a metal fabrication plant aluminum is received in rolls. The aluminum sheet metal in these rolls is 1mm thick. The width of the sheets is 60 cm. The rolls have an outer diameter (OD) of 90 cm. The aluminum sheet is wrapped around a plastic wheel, which makes the inner diameter (ID) of the coil 40 cm. The plant makes square pipes from the aluminum.
a) Find the total length of the coil.
b) If the coil is pulled at a rate of 180 ft/min find the angular velocities of the coil in the beginning and at the end.
c) Calculate the angular acceleration as the coil unwinds.
d) If the density of aluminum is 2.7 grams per centimeter cube, find the mass of the
coil.
PROBLEM 4
In a metal fabrication plant square aluminum pipe is made from long rolls of sheet metal. As the continuous pipe comes out of the machine it is traveling at a speed of 1 m/s. It is cut into lengths by a Flying Saw. The Flying Saw starts from rest and accelerates. It takes 2 meters for the pipe and saw to be moving at the same speed. The saw continues to move forward (now with constant speed) and in addition moves sideways at V=2 m/s to cut the pipe. This movement that both objects are moving together lasts 0.1 seconds.
a) Find the acceleration of the saw.
b) During this acceleration, the saw has two dimensional motion. Find
the mathematical equation for this motion and draw this two dimensional path
on a Cartesian coordinate system.
c) If the cutting takes 1/10 of a second, find the total distance that the saw has to
travel.
PROBLEM 5
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In a steel mill blast furnace structural support, a ring of mass M is held by ten supporting beams, as shown in the Figure. Discuss the necessary conditions to assure stability and durability of the structure using conditions of equilibrium.
PROBLEM 6
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A truck bed of total mass M =7500 kg, is loaded with two fans of mass M = 7500 kg each. (a) What is the force applied to each tire by the ground? Find the net torque applied to the last tires in the back of the truck. Use the given drawing. (c) What force must the truck's engine apply to pull the bed with an acceleration of 1.5 m/sec/sec. (ignore the mass of the engine and cockpit.) {Take the length of the flatbed L=60 ft or about L=18.3 m, and x=2 meters.}
PROBLEM 7
Draw a Free-Body Diagram for the Crane above.
PROBLEM 8
Some industries have to be concerned about
the cleanliness of their exhaust gasses. Electrostatic participators are often
used to remove particulate from the gas. The electrostatic participator has
charged plates that attract the particles. The particles stick to the plates.
If the dust collected on the precipitator plates is subsequently pulled away
from the plates it goes back into the gas and the precipitator accomplished
nothing. The tensile strength is the force required to tear the dust from the
plate. It is therefore, very important to measure the tensile strength of the
dust layers involved. A method using an electric field has been devised to
measure the tensile strength of the dust. The electric field induces a charge
on the exposed surface of the dust layer, and then it acts on that charge to
create the tensile force. The tensile force pulls on the surface particles
against the forces of cohesion that exist between the particles in the dust
layer is:
T = e 0
E2
In which T is the tensile strength, E is the
electric field and e 0 is the
permittivity of free space (8.85 x 10-12 in M.K.S. units).
a) Find the electric potential needed to
overcome the tensile
strength of 5Nm-2 , if the separation between the
plates is 5cm
(refer to figure
below).
b) Make a graph of T versus E2
for the values of T from 3Nm-2 to
8Nm-2.
PROBLEM 9
A dust particle of mass 1.6 X 10-10
g and charge 5X 10-6 Coulomb/gram exists between the plates of the
device used to measure the tensile strength of the dust layers on the plates of an electrostatic precipitators explained in problem 8.
The field across the plates is 3 kV/cm. Watch units in all parts of this problem.
It may be best to convert to S.I. units.
- What is the electric force on the particle?
- Is the gravitational force significant in this
situation? Why or why not?
- Given a distance between the plates of 5 cm,
how long does it take for a dust particle starting from rest, to get to
the opposite plate?
Problem 10
In the device used to measure the tensile
strength of the dust layers on the plates of an electrostatic precipitator an
electrostatic precipitator described in problem 8, a LASER beam is used to observe
the onset of the dust breaking away from the plates.
The dust particles are uniformly sized and
there are 1000 particles per cc in the air.
The distance across the plates is 8 cm.
On average, how far will the beam travel
through the air before hitting a particle?
PROBLEM 11
A Scanning Mobility Particle Sizer ( SMPS ) is a device developed by Southern Research Institute to determine the concentrations and size distributions of particles with diameters smaller than one micrometer (1m ). See the figure below.
If all particles enter the chamber with the same charge and initial velocity, find the ratio of the distances that the particles of sizes 1m and 0.1 m fall on the central rod from the top under the influence of the electric field E established across the chamber. (Consider the particles spherical and of the same density.)
PROBLEM 12
An electronics firm specializes in so-called
electronic Black boxes. These are electronic circuits mounted on bread boards
with specific input and output. To protect these boards they are incased in a
silicone rubber potting compound called STYCAST 4952.
Discuss the desired thermal and electrical
properties of such a compound.
PROBLEM 13
An electronics firm specializes in so-called
electronic Black Boxes. These are electronic circuits mounted on bread boards
with specific input and output. To protect these boards they are incased in a
silicone rubber potting compound called STYCAST 4952.
What is the maximum electrical potential
difference that can be applied across a black box filled with STYCAST 4952 of
length 25 cm? The dielectric strength of STYCAST 4952 is equal to 21.7KV/mm.
PROBLEM 14
The weather airplane that travels to the eye of hurricanes are equipped with a radar system that enables it to gather information about the path, pressure, etc. of the hurricanes.
The casing of this radar, which is constructed like a huge football, is made up of two layers of plastic with a honeycomb structure in between. Discuss the advantage of using this type of structure for the casing of radar.
HONEYCOMB STRUCTURE
PROBLEM 15-20
**For problems 15-20 refer to the given table.
The pilot of an airlines
is given flight data on a screen. This data is refreshed every 3 minutes. When
approaching an airport for a landing, the motion of the plane is at a steady
pace in lowering its speed and elevation. The table shows some of the data the
pilot saw. It also contains many blank boxes where data should be located.
15 - Finish filling out the table.
16 – Find the constant acceleration during
the first 33 minutes of the flight (in mi/hr squared and m/sec. squared).
17 – Find the constant acceleration during
the last 3 minutes, when the motion of the plane comes to a halt.
18 – Find the average velocity in this
process.
19 – Graph Altitude vs. Temperature (in
degree Celsius)
20 – Graph Altitude vs. Distance to
Destination
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TEMPERATURE |
ALTITUDE |
GROUND SPEED |
DISTANCE TO DESTINATION |
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0F |
0C |
ft x 1000 |
m |
mi/hr |
km/hr |
mi |
Km |
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-57 |
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36 |
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510 |
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190 |
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-47 |
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33 |
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480 |
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-37 |
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30 |
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450 |
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-27 |
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27 |
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420 |
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-17 |
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24 |
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390 |
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180 |
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63 |
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0 |
0 |
0 |
0 |
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Problem 21
Cutting
time for Turning, Boring and Facing
A Lathe is an important tool used to shape
metal. The cutting time for turning, boring, and facing a metal piece can be
determined by using the following relationship:
T=L/(F)(N)
Where:
T= Time in minutes
L = Length of cut in inches
F = Feed in inches per revolution
N = Lathe spindle speed in RPM
a) If the feed rate is 0.01" per revolution,
how many revolutions will be necessary to cut a 6" piece?
b) If the RPM is 600, how much time does it
take to do the cut?
c) What is the feeding speed?
PROBLEM
22
CENTER
OF GRAVITY OF ANY FOUR-SIDED FIGURE
Divide each side in 3 equal parts. A line is then drawn through each pair of division points next to the point of intersection A,B,C and D of the side of the figure. These lines form a parallelogram EFGH. The intersection of the diagonals EG and FH locate the center of gravity.
Explain why this works?
Problem 23
The block and tackle is used to lift heavy
objects with a smaller applied force. In the diagram the applied force (F) is
lifting the heavy object (W). The disadvantage in using the block and tackle is
the applied force (F) must move a distance greater than the object (W).
Show that the velocity with which (W) will
be raised equals 1/5 of the velocity of the force applied at (F).
Problem
24
A casting weighing 150kg is to be lifted by means of a crane. The casting is lifted 3 meters in 12 seconds. What is the horsepower developed?
Problem
25
Using method of moments, find the reactions at the supports of the following
beam. The mass of the beam is 50kg. (forces are in
F1=500, F2=200, F3=100
X1=2, X2=1, X3=2 and XT=10.
INTRODUCTION
TO PROBLEMS 26 AND 27
In a machine shop many of the machines
operate using a rotating spindle. The spindle speed and cutting speed are
related through the following equation:
N = V/ Pi x D
Where:
N=number of revolutions per minute for
spindle
D=cutting diameter in meters
V=cutting speed in meters/minute
PROBLEM
26
The cutting speed for turning a 5-inch
(127.5 mm) diameter metal cylinder has been found to be 600fpm (182.9m/min).
Calculate the lathe spindle speed both using inch and metric units.
PROBLEM
27
Calculate the cutting speed in units of feet
per minute, meter per minute, and meter per second if the spindle speed of
(19.05 mm) inch drill is 450 rpm.
A 0.75 inch (19.05mm) drill is 450 rpm.
PROBLEM 28
A steel foundry
wants to make a bid to construct T-shaped pipe. They need to determine the
amount of steel in each pipe to determine the cost. The procedure for making
the pipe is to build a mold with sand core. The dimensions are given in the
diagrams.
- What volume of the molten iron is
needed in order to make the pipe?
- Calculate the amount of additional
molten iron needed to compensate for shrinkage due to
cooling from 15000 c to room temperature. The coefficient of
linear expansion of iron is 12x10-6/ oc.
- Find the total mass of iron used in
the process. Take density of iron 7.01 gm/cm3 at 1500oc.
Z1 =
1.5m
Z2 =
1.5m
X = 0.8m
R om = 30 cm
R im = 28 cm
R ob = 20 cm
R ib = 18 cm
Acknowledgment
The author would like to thank the National Science Foundation for their
support of this project. In addition the thanks go to the following companies
and their representatives that allowed me to tour their facilities and helped
with the writing of the problems and also the organizations that were very
helpful with writing and finalizing these problems:
Ogihara, Process Equipment, Mason Industries, US Steel
(Fairfield Works), Southern Research Institute, Southern Company, International
Enterprises, Honeywell, Jordan Machine, Anniston Landfill, Baron Fan, ACIPCO,
UAB, Auburn University, Jeff State Office of Governmental Relation and Grants Management,
Jeff State Division of Math, Phy and Engineering,
Jeff State Division of Technology, TYC-21 Region 11, Seminole Community College
and Central Alabama Community College.