Time and Date Stamps (logged): 03:47:07 08-29-2008 ¯²Ÿ³¶Ÿ¯¶¯·Ÿ±¸Ÿ±¯¯· Precalculus II

University Physics (Phy 231, Phy 241) Test 1

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:

Directions for Student:

Test Problems:

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

.

.

.

.

.

.

.

.

.

.

Problem Number 1

An Atwood machine consists of masses of 1.2 Kg and 1.272 Kg hanging from opposite sides of a pulley.

.

.

.

.

.

.

.

.

.

.

Problem Number 2

If the velocity of an object is given by v(t) = .08 m/s^3 t^2 + .4 m/s^2 t + 3 m/s, then if the position x is 80 m when t = 0, find the acceleration function a(t) and the position function x(t).

.

.

.

.

.

.

.

.

.

.

Problem Number 3

A ball reaches a ramp of length 106 cm with velocity of 24 cm/s. It accelerates uniformly along entire length of the ramp in 5.7 seconds. What is its acceleration?

 

.

.

.

.

.

.

.

.

.

.

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.

.

.

.

.

.

.

.

.

.

.

Problem Number 5

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 .08 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 = 13 degrees?

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

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

 

.

.

.

.

.

.

.

.

.

.

Problem Number 6

A system consists of a cart pulled along a constant-velocity ramp by the force of gravity on a single paper clip, whose mass is much less than that of the cart, attached by a thread over a pulley with negligible friction. If the system accelerates at 5.3 cm/s2, and if F = m a describes the relationship among net force F, mass m and acceleration a, give the acceleration of each of the following:

The same system but with 5 paper clips instead of one.

The same system but with a single paper clip and a cart of twice the mass.

The same system but with a single paper clip with a cart of half the mass.

The same system but with 12 paper clips and a cart of 3 times the mass.

What would be the acceleration of the same system but with a number of paper clips whose mass equals that of cart?

How would the slope of a graph of acceleration vs. number of paper clips for the original system (for a small number of paper clips) compare with the slope for a system with double the cart mass, and how would it compare with the slope of a system with 12 times the cart mass?

.

.

.

.

.

.

.

.

.

.

Problem Number 7

A cart of mass 240 grams is temporarily held stationary on an incline at 3.1 degrees to horizontal. 

.

.

.

.

.

.

.

.

.

.

Problem Number 8

Solve the following problem by using the basic equations of kinematics. If an automobile accelerating at - 2 m/s/s comes to rest after traveling through displacement 26 meters, then what are the values of the five standard kinematic quantities? Interpret each quantity you have calculated in terms of the situation.

.

.

.

.

.

.

.

.

.

.

Problem Number 9

Explain why the area under a position vs. time graph, between two clock times, is equal to the distance traveled between those two times.