Time and Date Stamps (logged): 01:27:07 08-29-2008
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Precalculus II
Principles of Physics (Phy 121) Final Exam
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
A mass on a spring is observed to complete 49.998 cycles of oscillation every
minute. The spring constant is known to be 1000 Newtons/meter. What is the mass, in
kilograms?
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Problem Number 2
What are x and y the components of the displacement
vector obtained when we add the two following displacement vectors:
- vector A, with x and y components 9.2 meters and
-8.3 meters, and
- vector B whose x and y components are 2.9 meters
and 8.5 meters?
What are the magnitude and angle of the resultant
vector?
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Problem Number 3
What is the KE change of an
object of mass 6.5 kg as its gravitational PE decreases by 74 J if at the same time it also
does 52 J of work against the net nongravitational force?
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Problem Number 4
If an object of mass 2.9 Kg and initially at rest is pushed by a net force of 18.85 Newtons
for 9.3 seconds, how far does it travel and what is its final velocity?
- How much work is done, and what is its kinetic energy?
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Problem Number 5
The velocity of an object increases at a
constant rate of 43 meters/second per second.
- How long will it therefore take the object to
increase its velocity by 7 meters/second?
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Problem Number 6
The gravitational effect of the Earth can be
thought of as being spread out over larger and larger spheres, each concentric with the
Earth. The greater the area over which the field is spread, the less the strength of the
field.
At the radius of the Earth, the field strength is
9.8 m/s ^ 2.
- What would be the field strength at twice the radius
of the Earth?
- What would the strength be at 4 times the radius of
the Earth?
- If the radius of the Earth is 6400 km, then what
would be the strength at a distance of `a kilometers from its center?
- At what distance from its center does the
gravitational field of the Earth fall to half its value at the surface?
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Problem Number 7
What is the acceleration of an object of mass 900
kilograms in circular orbit about a planet of mass 7 *10^ 23 kilograms at a radius of 20000
kilometers?
- How fast must be object be traveling if it is to
remain in a circular orbit about the planet?
- How long will it take the object to complete one
orbit? Neglect any difference between the radius of the orbit and the distance
between the object and the center of the planet.
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Problem Number 8
A mass of 7.1 kg is suspended from a spring with force constant 61 N / m.
- If the mass is released from rest at a point .69 meters from equilibrium, what
will be the angular frequency of its motion (angular frequency is the angular velocity of
the point on the reference circle which models the motion)?
- What is the average speed of the object between t=-.001 sec and t = .001 sec?
- How are the two velocities related and why?
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Problem Number 9
A mass of 11 kg on a level tabletop is attached by
a light string to a mass of 4 kg; the second mass is hanging vertically from a pulley.
The string runs from the first mass in the horizontal direction to the pulley. The pulley
is considered to be light and frictionless.
If there is no friction anywhere in the system:
- What is the net force on the system?
- If the system is released from rest, how much work
is done on it by the net force as it moves 3.8 meters under the influence of this force?
- What therefore will be its kinetic energy after
having moved the 3.8 meters?
Answer the same questions if the only friction in
the system is on the mass on the tabletop, and if the coefficient of friction between the
mass and the tabletop is .15.
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Problem Number 10
What vector of magnitude 4.3 must be added to the
velocity vector A = < -1.44 m/s, 8.28 m/s> in order to obtain a vertical vector R?
Answer by giving the magnitude and angle of the vector to be added.
- (Note on notation: <u,v> stands for a vector
whose x component is u and whose y component is v.)
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Problem Number 11
An object of mass 16 kg experiences a variable force F(t) (here F(t) indicates
function notation, not multiplication of F by t; F(t) is the force at clock time t)
for 6 seconds.
If the average force over this time is 896 Newtons,
- Use Newton's Second Law and your knowledge of uniformly accelerated motion to find the
change in the object's velocity.
- Use the Impulse-Momentum Theorem to obtain the same result.
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Problem Number 12
An object of mass 11 kg is subjected to a variable force F(t) (here F(t) indicates
function notation, not multiplication of F by t; F(t) is the force at clock time t) for .8
seconds.
During the .8-second time interval, the force increases linearly from 0 to 77 Newtons,
then decreases linearly back to 0.
Find the change in the object's velocity.
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Problem Number 13
An object is moving at a constant velocity of 4 m/s before an acceleration phase, and
at another constant velocity after the acceleration phase.
- If during the acceleration phase the velocity changes at a rate of 3 m/s
per second, and if the acceleration phase lasts 9 seconds, then what will be the increase
in velocity?
- What will be the second constant velocity?
- What will be the average velocity?
- How far will the object travel during the acceleration phase?
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Problem Number 14
Four masses, each of 8.699 /4 kilograms are placed on
a massless X shaped frame, one mass at the end of each crossbar. The system rotates about
the center, and each mass is .6999 meters from the center. A rotation-producing torque of 12.99
meter Newtons is applied to the system.
- Suppose that each mass was subjected to a force
which would supply 1/4 of this torque. What would be the total of all these forces?
- What would then be the acceleration of each mass?
- What would be the angular acceleration of the
system?
Since all the masses are at the same distance r
from the axis of rotation, the quantity mr ^ 2, where m is the sum of all the masses, is
easily calculated.
- What is the ratio `tau /mr ^ 2 for this system?
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Problem Number 15
Using the approximation that 1 meter per second is
about 2.3 miles per hour, find the centripetal acceleration of a 1493 kilogram automobile
moving at 11.99 miles per hour on a circular track whose radius is 143 meters.