Time and Date Stamps (logged): 12:44:20 05-21-2012 °±Ÿ³³Ÿ±¯¯´Ÿ±°Ÿ±¯°± Precalculus II

University Physics (Phy 231, Phy 241) 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.). 

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Instructions:

Directions for Student:

Test Problems:

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Problem Number 1

Given that the gravitational potential energy of a mass m at distance r from the center of a planet of mass M is PE(r) = G M m / r, find the derivative dPE / dr. 

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Problem Number 2

A simple pendulum has a length of 1.13 meters.  What is its period of oscillation?

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Problem Number 3

What is the equation of motion of simple harmonic oscillator with mass m and restoring force constant k which is given an initial velocity v0 at position x0 at clock time t = 0?   What are the expressions for its velocity and acceleration functions v(t) and a(t)?

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Problem Number 4

The force exerted by a certain rubber band at stretch x is given by the function F(x) = k x^ .7, with k = 170 N / m^ .7.

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Problem Number 5

A mass at the end of a spring oscillates with a frequency of 1.11 cycles / second. When a mass of 370 kg is added it oscillates with a frequency of .41 cycles/second.   What is the added mass?  code `t

 

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Problem Number 6

A uniform disk is growing in such a way that its radius increases by .7 cm every minute.  The mass density of the disk is 5 grams per cm^2 of cross-sectional surface area.  If I(r) is the moment of inertia of the disk when its radius is r, then what are dI / dr and  dI / dt at the instant the radius is 55 cm?

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Problem Number 7

If a mass of 4 kg moving at 8 m/s collides with a mass of 9 kg moving at -3 m/s, and the two masses are 'stuck together' after collision, then what is their common velocity after collision?  Is this collision possible for the system consisting of the two masses without the conversion of some internal source of potential energy?

 

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Problem Number 8

If a simple pendulum of length .89 meters is subjected to a restoring force of 8.2 Newtons when displaced .04717 meters from equilibrium, what is the mass of the pendulum?   What will be its period of oscillation?

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Problem Number 9

If a simple harmonic oscillator of mass .61 kg is subjected to a restoring force of 3.9 Newtons when displaced .0427 meters from equilibrium, what will be its KE and its PE at equilibrium and halfway to equilibrium if it is released from rest at a displacement of .3904 meters from equilibrium?

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Problem Number 10

When masses of  60, 120 and 180 grams are hung from a certain rubber band its respective lengths are observed to be 39, 48 and 57 cm. What are the x and y components of the tension of a rubber band of length 54.21 cm if the x component of its length if 52.388 cm?

What force directed at 113 degrees, when added to this force, will result in a horizontal net force?

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Problem Number 11

We wish to examine orbital velocity, kinetic energy and potential energy at a distance of 1.9 Earth radii from center.  Imagine that you are orbiting Earth at this distance.

G = 6.67 * 10^-11 N m^2 / kg^2, Earth mass is about 6 * 10^24 kg and Earth's radius is about 6400 km.

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Problem Number 12

What is the centripetal acceleration of a satellite orbiting at a radius of 10800 km from the center a certain planet if it is moving at 10100 m/s in that orbit?  What is its orbital period (i.e., how long does it take to complete an orbit)?

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Problem Number 13

A cart of mass 1.7 kg coasts 70 cm up an incline at 6 degrees with horizontal.   Assume that frictional and other nongravitational forces parallel to the incline are negligible.

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Problem Number 14

Explain how we used a rubber band and a ‘rail’ to demonstrate the conservation of the F `ds quantity.

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Problem Number 15

Write down the four basic equations of uniformly accelerated motion. Specify which two are considered the most basic, and explain their meaning in commonsense terms. Show how to use these two equations to derive the equation for 61 in terms of `dt, v0 and a.