Precalculus II

Time and Date Stamps (logged): 01:32:08 08-29-2008 ｯｰ浚ｱ浣ｷｯｷ浤ｸ浤ｯｯｷ Precalculus II

General College Physics (Phy 201) 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.).

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:

. . . . . . . . . . . . . . . .

Problem Number 1

Sketch a force diagram depicting weight and normal force for a glider gliding down an inclined air track. Indicate an x axis parallel to the incline and a y axis perpendicularto the x axis. Sketch the force vectors to scale and indicate their x and y components. Also sketch the net force vector, in the appropriate direction and also to scale.

Sketch a diagram to show the forces that would result if a horizontal force equal to half the weight of the glider was exerted in a direction that would tend to push the glider up the incline. Indicate the x and y components of all these vectors. Sketch all vectors and all components to scale.

We know that for an air cart gliding along an incline, the force that accelerates it is equal to W sin(`theta), where W is the weight of the cart and `theta the angle of the incline with horizontal.

If the force on the glider was W, what would be its acceleration?

If the acceleration of a mass is proportional to the net force acting on it, then

what should be the acceleration of the glider under the influence of a net force of .04 W?

what should be the acceleration of the glider under the influence of net force W sin(`theta)?

What should be the acceleration of the glider for `theta = 3 degrees?

What is the slope of the incline corresponding to this angle?

Explain why, for small angles, acceleration is proportional to slope.

Problem Number 2

What is the gravitational field strength of Earth at a distance of 2.3 Earth radii from center? Solve in two ways:

First solve using proportionality and our knowledge that at 1 Earth radius the field strength is 9.8 m/s^2.
Then solve using the fact that the mass of Earth is about 6 * 10^24 kg, its radius about 6400 km and the universal gravitational constant 6.67 * 10^-11 N m^2 / kg^2.

Problem Number 3

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.

Problem Number 4

A uniform sphere of mass .71 kg and radius 23 cm is constrained to rotate on an axis about its center. Friction exerts a net torque of .0004232 meter Newtons on the system when it is in motion. On the disk are mounted masses of 21 grams at a distance of 16.1 cm from the axis of rotation, 14 grams data distance of 13.34 cm from the axis and 47 grams at a distance of 8.51 cm from the axis. A uniform force of .008 Newtons is applied at the rim of the sphere at 23 cm from the axis of rotation.

As the sphere rotates through 5 radians, what will be its change in kinetic energy? Find your result by work\energy considerations only.
If the sphere starts from rest what will be its final angular velocity?
What will be the kinetic energy of each of the masses at this final angular velocity? Does the sum of these kinetic energies equal the total kinetic energy calculated earlier?
If the force was applied by a descending mass attached to the sphere by a light string around its rim, what was the mass and how far did it descend? You may assume that the mass is negligible compared to the mass of the sphere.

Problem Number 5

If a mass of 7 kg moving at 4 m/s collides with a mass of 7 kg moving at -4 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?

Problem Number 6

A neutron star might have about five times the mass of our Sun, around 10^31 kg, packed into a very nearly perfect sphere of radius roughly 10 km. If you suddenly appeared at the surface of a Neutron star you would almost instantly become a part of that nearly perfect sphere (though you would probably be integrated nearer to your point of contact, you might think of yourself as almost instantly forming a thin coat, like a coat of paint, over the surface of the star).

Suppose you somehow managed to retain your mass and some form of structural integrity and began walking across the surface of the star.

If there was a long incline on the star (another impossibility), with the far end of the incline 1 cm higher than the near end, how long would it take you to climb the incline? Assume that you can sustain a production of 143 Joules of useful energy per kg of body mass for 8 hours each day.