PHYSICS 241 -- Assignment 12
Due before class on 10/21 (I will review in class)

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1) Four blocks abut eachother on a flat table.  They have masses 
of 4 kg, 3 kg, 2 kg, and 1 kg.  A 50 N force is applied to the
4 kg block.
    a) Sketch the problem
    b) Draw free body diagrams for each of the four blocks.
    c) Calculate the acceleration of the system.
    d) Calculate the force that each block exerts on its neighbor.
    
2) Three blocks of equal mass abut eachother on a ramp
of angle 60 degrees.  The middle block is made of wood and
has a friction coefficent of 0.3 with the ramp.  The two blocks on
the end are made of teflon and have a friction coefficient of 0.1
with the ramp.  
    a) Sketch the problem
    b) Do the three blocks remain together as they slide down the ramp?
    Explain.
    c) What is the acceleration of the two blocks that remain together?
    d) What force do they exert on eachother?
   
3) Look up Atwood's machine (it's all over the net).  Analyze the simplest
Atwood's machine consisting of a frictionless pulley and two masses m1 and m2.
    a) Sketch the problem
    b) Draw a free body diagram for each mass
    c) Calculate the acceleration (a) of the system for arbitrary m1 and m2.
    d) Calculate the tension (T) in the string for arbitrary m1 and m2.
    e) Assume m1=m2=1 kg.  What are "a" and "T"?
    f) Assume m1=1 kg and m2= 3 kg.  What are "a" and "T"?
    g) Assume m2 >> m1.  What are "a" and "T" (in terms of m1 and m2).

4) Three masses of mass 3, 4, and 5 kg are attached with a string on a ramp 
with angle 30 degrees with horizontal.  The 5 kg mass is furthest up
the ramp and the 3 kg mass is lowest.  Another string is attached to the 
5 kg mass and runs over a pulley to another 10 kg mass hanging vertically.
The 10 kg mass is released.  
    a) Sketch the problem
    b) Assume there is no friction.  Which way do the masses move?
    c) For this case, calculate the tension in each string and the
    acceleration of the set of masses.
    d) Repeat the problem assuming that the ramp angle is changed to 70
    degrees.  
    e) Return the ramp angle to 30 degrees and include a friction
    coefficent of 0.2 of each block with the ramp. Calculate all the 
    tensions and acceleration of the masses.