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 Which constraints are binding?

It takes the planet Jupiter 12 years to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun is 1.5 x 1011 m.)

p2something.png An object side a distance d down and incline of height ∆y as shown.  If the coefficient of friction between the surface and the object is 0.250, determine the work done by friction. m = 5.00 kg, d = 9.00 m,  and ∆y = 3.00 m.

A worker pushes a 8.0 kg crate across a level surface with a force of 35.0 N directed at an angle of 25.0° downward from the horizontal. Determine the work done by gravity after the crate is pushed 12.0 m.

What is the kinetic energy of a car of mass 1750 kg traveling at 25 m/s?

The force on an electric charge in an electric field is F = qE where F is the force, q is the electric charge, and E is the electric field.  Determine the speed of a proton (charge = 1.6×10-19 C, mass = 1.67×10-27 kg) after it has been accelerated, from rest, a distance of 0.25 m though an electric field of 2.0×106 N/C. 

p2something.png An object slides a distance d = 9.00 m down a frictionless incline of height ∆y = 3.00 m as shown.  Determine the speed of the object at the bottom of the incline if it starts from rest.

p10(1).png A simple pendulum of length L = 0.75 is pulled back to an angle θ = 35.00 and released.  What is its speed of the pendulum at the bottom of its oscillation?

A 500 kg ore cart traveling at 12.0 m/s on a level track is stopped by a spring of spring constant 35,000 N/m mounted horizontally at the end of the track.  By how much does the spring compress in stopping the car?

A 1500 kg train car traveling east at 3.0 m/s collides with, and couples to, a 1200 kg train car traveling west at 2.0 m/s.  What is the speed of the train cars after coupling?