EXAM 3                      December 4, 1996                          PHYS 207

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No notes, books, etc. may be used during this exam.

g = 9.8 m/sec2Radius of the earth = 6.38 x 106 m The mass of the electron is 9.11 x 10-31 kg.
For all problems, place the equations representing the physics principles you are using in the box on the page. You may use the general form of the equation or the form you get applying the principle to the problem at hand. If no diagram is applicable to a problem, write "none" in the diagram section.

1. (10 points) Explain how, knowing

x = x0 + v0 t + ( 1 / 2 ) a t2 ,

you can determine both of the equations governing motion under constant torque. Be sure to state explicitly the relations you use between linear variables and angular variables. 2. (30 points) The following question was asked on sci.edu last week: 

Subject: ***Help With Physics Question Requested***
Date: 24 Nov 1996 03:22:01 GMT
From: *************** (************)
Organization: Student
Newsgroups: sci.edu

I have a physics question for all physics students out there,

2 blocks of wood of equal mass are set up an equal distance away from 2 guns.
Each gun contains a bullet of equal mass, one is rubber one is aluminum. 
When fired the rubber bullet bounces off the block of wood while the
aluminum bullet imbeds itself in the wood.  The bullets both travel at
equal velocities and the surface on which the blocks sit is ice so
friction is minimal.  Which block of wood would travel further?

Any help on this question is greatly appreciated.
The question was answered as follows: 
Subject: Re: ***Help With Physics Question Requested***
Date: Sun, 24 Nov 1996 12:56:45 GMT
From: *****************************
Organization: Internet Connect Services
Newsgroups: sci.edu

The block with the aluminum bullet will travel further due to the law
of conservation of momentum.  The rubber bullet bouncing off the block
has some momentum that isn't present in the aluminum bullet-block
system.
What is your reaction to this answer? Be as quantitative as possible. For definiteness, assume that the rubber bullet rebounds with half the speed that it had coming in. 3. (From homework, 30 points) A block is on a horizontal surface (a shake table) that is moving horizontally with simple harmonic motion of angular frequency omega. The coefficient of static friction between the block and the surface is mus. How great can the amplitude of the simple harmonic motion be if the block is not to slip along the surface?

Diagram: Principles:











4. (30 points) A solid cylinder of radius R and mass M rolls without slipping down a plane inclined at angle theta. The coefficient of static friction is mus. What is the maximum value of theta that permits the cylinder to roll without slipping? The moment of inertia of a cylinder about its central axis is I = (1/2) M R2 .

Diagram: Principles:











Use this page if necessary to continue any of the problems. Be sure to label the problem number.