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Precalculus II
Principles of Physics (Phy 121) Test_2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
Using proportionality, find:
- The field strength at twice the radius of the Earth
from its center.
- The strength at 4 times the radius of the Earth from
its center.
- The strength at a distance of 22900 kilometers from its
center.
- The distance from Earth's center where the
gravitational field of the Earth is half its value at the surface.
You may use the information that the acceleration
of gravity at the surface of the Earth is 9.8 m/s^2 and the the radius of the Earth, which
is approximately 6400 km.
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Problem Number 2
A tower rises from its base at the surface of the
Earth, a distance of 6400 km from the center, and rises an altitude of 800 kilometers above
the surface. An individual of mass 61 kg wishes to climb the tower.
- How much would the person weigh at the bottom and at
the top of this tower?
- If the average weight of the person during the climb
was equal to the average of the two weights just found, and if the person was capable of
an average sustained power output of 1.42 watt/kg for 8 hours per day, then how many days
would be required for the climb?
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Problem Number 3
Imagine that you are orbiting a neutron star whose
mass is 50 * 10^30 kilograms at a distance of 24 kilometers from its center.
- Find the force exerted by gravity on a one kilogram
mass in this orbit.
- Find the force exerted by gravity on a one kilogram
mass orbiting one kilometer further from the center of the planet.
- What is the difference in the forces?
- What is the velocity of the first orbit?
- What is the velocity of the second orbit?
- By how much does the orbital velocity of the first
object exceed that of the second?
From your first result, which gives the force
change per kilometer, determine the average force gradient (force change per unit of
distance), in Newtons per meter, for one kilogram masses between 24 and 24+1 kilometers
from the center of the neutron star.
- Give the approximate force difference you would
therefore expect between one kilogram of your left shoulder and one kilogram of your right
shoulder, assuming that one shoulder is .35 meter further from the star than the other.
- How much force do you think your shoulders can stand
without being torn from your body?
- Discuss the implications of the force difference you
calculated for your structural integrity.
From your second result, determine the average
velocity gradient, in (m/s) per meter, between orbits at 24 km and at 24+1 km from the
center.
- What therefore would be the difference in the
velocities of your two shoulders, assuming that they did indeed orbit separately.
- Give the approximate time it would therefore require
the shoulder closer to the planet to 'lap' the other.
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Problem Number 4
An object is moving on a circle whose radius is
14 meters.
- At what rate, in radians/second, is the angle of
the radial line from the center of the circle to the object changing if the object
completes 28 revolutions per second?
- How fast is the object therefore moving?
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Problem Number 5
An object of mass 35.99 kg is moving at 16.99 m/s on a
circle of radius 7 meters.
- What is its centripetal acceleration and what is the
centripetal force holding it in the circle?
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Problem Number 6
A massless disk is constrained to rotate about an
axis through its center and perpendicular to its plane. Circles concentric with the disk
are drawn on the disk, the first having radius 11.3 meters, the second twice and the third
three times that radius. Around each circle, masses of 7 kilograms are evenly
distributed, with 2.825 / `pi meters of arc between masses.
- A net torque of 1919 meter Newtons is applied. What
angular acceleration results?
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Problem Number 7
If 10 gallons of paint are uniformly
spread out over the surface of a sphere of radius 9.1 meters, how much paint is applied per
square meter?
- If the radius doubles, by what factor does the
amount per square meter change?
- If the radius quadruples, what is the factor?
- If the radius is 16 meters, what is the factor?
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Problem Number 8
What is the moment of inertia of a disk that
accelerates from 4.7 radians/second to 13.59 radians/second in 6.2 seconds when subject to a
torque of 5.599 meter Newtons?