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Precalculus II
Principles of Physics (Phy 121) Test_Set_9
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Date and Time are 02-15-2001 17:26:32
Signed by Learning Lab Attendant: ______________________
Date and Time: ______________________
Attendant:
Test is to be taken without reference to text or outside notes.
Calculator is allowed.
No time limit but test is to be taken in one sitting.
Please place test in Dave Smith's folder when completed.
Student:
Completely document your work.
Undocumented and unjustified answers may be counted wrong.
Besides undocument and unjustified answers, if wrong, never get partial credit.
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Problem Number 1
If we move an object from equilibrium to a point .24 meters from equilibrium,
against a net restoring force governed by the constant k = 35 Newtons/meter, how much work
is done?
- How much additional work would be required to then move the object to a point .81
meters from equilibrium?
- If the object was released from rest at this position, what then would be its
kinetic energy at the point .17 meters from equilibrium?
- What would be the object's kinetic energy at its equilibrium point?
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Problem Number 2
What is the mass in kilograms of an object if, when suspended from an ideal
spring whose restoring force constant is 390 Newtons/meter, the mass completes 117.6
cycles every minute?
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Problem Number 3
Suppose that an object on a spring has mass m and
the force constant of the spring is k. If the object is displaced a distance A from its
equilibrium position and released, the y coordinate of its position at time t will be the
same as that of a point moving with angular velocity
- angular velocity = `omega = `sqrt(k/m)
on a circle of radius A (the y direction is taken
as the direction in which the object moves). Here k is the force constant (generally
measured in Newtons / meter) of the spring and m the mass of the object.
- If an object of mass 5 kilograms suspended from
a spring is released from rest at a point 9.5 meters below its equilibrium position,
and if the spring has force constant 1690 Newtons/meter, then how long does it take
the object to move through one complete cycle?
- If t = 0 when the object first passes upward through
the equilibrium position, then what will be its position at t = .1825 seconds?
- What will be its average velocity and kinetic energy
between t = -.001 sec and t = .001 sec?
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Problem Number 4
An object is released from rest at a distance of .33 meters below its equilibrium
point. If the object is subjected to a net restoring force with force constant 44 N
/ m, and if the mass of the object is 8.3 kg, then
- What is the centripetal acceleration, in m/s ^ 2, of the reference point on the
circle which models the resulting simple harmonic motion?
- What acceleration would you expect for the object at the instant it reaches an
extreme point?
- Explain in your summary why you would expect the object itself to undergo this
acceleration at the extreme positions in its cycle.