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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
We measure the velocity of an object to be 5 m/s.
From its effect in a collision with another object we determine that its momentum
must have been 145 kg m/s. What is its mass?
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Problem Number 2
What is the restoring force constant of an ideal spring if, when a mass of 25.45
kg is suspended the mass oscillates at .5555 cycles/sec.
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Problem Number 3
A mass of 14 kg on a level tabletop is attached by
a light string to a mass of 6 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?
- What is the acceleration of the system consisting of
the two masses and the string?
- What is the tension in the string?
- If the system is released from rest, use your
knowledge of uniformly accelerated motion to determine its velocity after moving 2
meters.
- If the system is released from rest, how much work
is done on it by the net force as it moves 2 meters under the influence of this force?
- What therefore will be its kinetic energy after
having moved the 2 meters?
- As the system moves 2 meters, by how much does its
gravitational potential energy change, and by how much does its kinetic energy change?
- If the system is moving in the direction of the net
force at 3.1 m/s, by how much will its velocity increase as it moves 2 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 .13.
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Problem Number 4
If velocity increases linearly from 4 meters per second to 13 meters per second in 7
seconds, what is the average velocity, and what is the distance moved in the 7 seconds?
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Problem Number 5
What is the acceleration of an object of mass 310
kilograms in circular orbit about a planet of mass 8 *10^ 25 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 6
A hoop of radius 12.1 meters and mass 1.5 kilograms is rotating at
.8 radians/second. While subject to no external forces, the hoop contracts to a radius of
7.2 meters without losing any of its mass.
- What will be its angular velocity at the new radius?
- What will be the ratio of its angular velocities and of its
moments of inertia after contracting as compared with before?
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Problem Number 7
What vector of magnitude 7.9 must be added to the
velocity vector A = < 3.32 m/s, .52 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 8
If an object of mass 6 kilograms, suspended by
a spring, is released from rest at a point 4.5 meters below its equilibrium position,
and if the spring has force constant `forceConstant Newtons/meter, then what will be its
average kinetic energy between times t = -.001 sec and t = .001 sec?
What is the average of the net forces on the object
at the equilibrium point its point of release? Using this average, determine the work done
on the object by the spring between its position of release and the equilibrium position.
Comment in your summary on the relationship between
your results and the conservation of energy.
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Problem Number 9
The momentum of an object of mass 23 kg is known to be -161 kg m/s.
What is the velocity of this object?
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Problem Number 10
A force vector has length 8 and is directed at
an angle with the positive x axis of 16 degrees. What are the lengths of the
force vectors in the x and y direction which would have the same effect as this force?
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Problem Number 11
During 1
minute, the velocity of an object increases by 3 meters/second.
- It is known that the velocity of the object will
eventually increase by 27 meters/second.
- If the rate remains constant, how many minutes
will be required?
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Problem Number 12
Find the centripetal acceleration of an automobile
moving at 3 miles per hour moving around a circular track of radius 179 meters.
- If the automobile has a mass of 1440 kilograms, how
much force is required to hold the vehicle in the circle?
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Problem Number 13
The gravitational field strength at the surface of the Earth, and at the
surface of the moon where g is 1.5 m/s^2?
If your mass is 60 kg, what is your weight on the surface of the Earth
and on the Moon?
What is the strength of the gravitational field on the surface of a
planet where you weigh 2000 Newtons?
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Problem Number 14
Assuming that no energy is
dissipated in the process and that no other forces act on the object, what velocity will
mass of 6.1 kg attain, starting from rest, as a rubber band does 75 J of work on it? What
will be the PE and KE changes of the system during this process?
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Problem Number 15
The energy gained by a certain object is equal to the work done on it.
- If the work is done by a constant 3 Newton force, over what distance
must the force be applied to an object, parallel to its direction of motion, in order for
the object to gain 19 Joules of energy?