p7.png Two objects are connected by a rope over a massless, frictionless, pulley. The coefficient of kinetic friction  the surface and m2 is m = 2.5.   Assume m2 slides up the ramp, and determine the Tension in the string connecting the masses for m1 = 40.0 kg, m2 = 10.0 kg, and q = 30.00

p3.png Two objects are pulled vertically upward against gravity as shown.  Determine the tension in the rope connecting the objects for m1= 6.0 kg, m2 = 4.0 kg and F = 150 N.

prob 9 pic.png Determine the acceleration  of the object above if the coefficient of kinetic friction between the object and the surface is 0.25 and F = 75 N , m = 15 kg, and θ = 300.

p11.png Determine the acceleration of the crate if coefficient of kinetic friction between the surface and the crate is 0.35, the mass of the crate is 25 kg, and the angle of the incline is 300.

p1.png Two objects are pulled across a frictionless surface as shown.  Determine the acceleration of the objects for m1 = 6.00 kg, m2 = 4.00 kg and F = 8.00 N.

Consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000  5000 units If your supplier decided to stop offering the quantity discounts you see above, and just told you that all items would cost $10 each, your economic order quantity would be

Suppose for the same problem as in the previous question, the profit per unit produced of X and Y was 8 and 4 dollars, respectively.  The appropriate objective function for this would be:

p4.png A way to simulate gravity in space is to shape the space station like a cylindrical shell that rotates, with the astronauts living on the inside surface as shown.  If the radius of the space station is 750 m, at what angular speed would it have to rotate so that the astronauts experience the same normal force standing on the station that they would on Earth?

A satellite of mass 500 kg undergoes a circular orbit of radius 8000 km and a constant speed of 7060 m/s.  What is the acceleration of the satellite?

For the next two questions, suppose you had the following output from LINGO for some linear program.    Variable            Value      Reduced Cost         X1         6.000000          0.400000         X2         0.000000          0.780000         X3         9.000000          0.120000         X4         0.000000          0.000000       Row    Slack or Surplus     Dual Price         1          0.000000          1.000000         2          0.000000          0.000000         3          2.000000          1.250000         4          1.000000          0.900000         5          0.000000          0.000000 The optimal value of the first decision variable is