Midterm 1
P2820 W2009  2:00pm February 12, 2009

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1 Betaman Returns

Crushed by the defeat dealt to him by the conniving Snydley Whiplash, Betaman throws a wrench at Snydley's helicopter hovering 400m above the ground, causing the helicopter to instantly lose power, partially.  The lift force provided by the helicopter blades now decays with time and is given in newtons by H(t)= 15 000 exp( -t /100), with t in seconds after the wrench hits.  The air provides a drag force proportional to velocity of magnitude Fd = k v , where k [in units of kg/s] varies with height above the ground as 197.5 -0.1 y, where y is the height in m.  The mass of the helicopter is 1600kg, and g=9.8 as usual.  
How fast is the helicopter falling when it crashes (2 sig figs)?

2 Atwood's machine over a table with an angle with friction

Block 1 of mass m1=2kg lies on a slightly rough table, with friction coefficient μ=0.1, and is connected by a non-elastic string running through a pulley to a second block of mass m2=1kg hanging vertically.  The pulley is a height h=5 above the origin.  Thus the string forms an angle θ with the horizontal.  θ changes as the blocks move, resulting in a non-constant tension.  Furthermore, the accelerations of the blocks are not equal in magnitude in general.  We can assume that block 1 stays on the table and doesn't lift off.  Block 2 absorbs moisture from the air, gaining mass at a rate of 0.005 kg/s (for block 2, use F= m a + dm/dt v).  For initial conditions x(0) = 5m, y(0)=4m,  and x'(0)=0, plot the position of block 1 for the first 3 seconds, and find how long it takes for block 1 to reach the end of the table (4 sig figs).