Time and Date Stamps (logged): 17:12:20 06-10-2020 °¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯ Precalculus II

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

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Instructions:

Directions for Student:

Test Problems:

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Problem Number 1

If a simple pendulum of mass 1.309 kg and length 55.99 cm is moving at 171 cm/s as it passes through the low point of its arc, what its its angular velocity about its pivot point at that instant?  What is the tension in the string of the pendulum?

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Problem Number 2

Prove that if the gravitational field strength at distance r from the center of a planet of mass M is G M / r^2, the work required to move a mass m from a point at distance r1 to a point at distance r2 from the planet with no net change in velocity is G M m ( 1/r1 - 1/r2).  Derive the expression for the velocity of an object in a circular orbit at distance r from the center of the planet.  Use this result to show that the KE change between circular orbits has half the magnitude of the PE change between those orbits.

 

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Problem Number 3

A uniform disk of mass .84 kg and radius 30 cm is constrained to rotate on an axis about its center.  Friction exerts a net torque of .09 meter Newtons on the system when it is in motion.  On the disk are mounted masses of 21 grams at a distance of 23.4 cm from the center, 6 grams data distance of 16.2 cm from the center and 48 grams at a distance of 10.8 cm from the center. A uniform force of .5 Newtons is applied at the rim of the disk in a direction tangent to the disk.  The force is applied for 3 seconds with the disk initially at rest.

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Problem Number 4

When masses of  55, 110 and 165 grams are hung from a certain rubber band its respective lengths are observed to be 34, 46 and 58 cm. What are the x and y components of the tension of a rubber band of length 55.06 cm if the x component of its length if 21.48175 cm?

What horizontal force, when added to this force, will result in a total force of magnitude 270 grams (a gram force is the force of gravity on a one gram mass)?

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Problem Number 5

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 6

A simple pendululm of length 2.9 meters and mass .32 kg is pulled back a distance of .206 meters in the horizontal direction from its equilibrium position, which also raises it slightly.  How much work must be done to accomplish this?

 

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Problem Number 7

Explain why the work required to stretch a spring or other elastic object with a linear restoring force, of form F = - kx, from its equilibrium position to displacement x is `dW = .5 k x^2, and why we hence say that this is the elastic potential energy of the object in this position.

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Problem Number 8

A white dwarf star might have about the mass of our Sun, around 2 * 10^30 kg, packed into a very nearly perfect sphere of radius roughly 1600 km (the radius of the Moon).  If you suddenly appeared at the surface of a dwarf star you would vaporize-they're hot, even if they are small.