p6(1).png A roller coaster makes an inside vertical circle as shown.  If the circle has a radius of 50.0 m and the car is traveling at 25 m/s, determine the normal force on a rider of mass 75 kg in the car.

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?

If demand and lead time are variable, as long as we carry safety stock we’ll have a 100% service level.

A hypothetical planet has a mass of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth?

A satellite is in circular orbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of the Earth is 6.38 x 106 m.)

For a spacecraft going from the Earth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel? Earth’s mass: Me = 5.98 x 1024 kg the Sun’s mass: Ms = 1.99 x 1030 kg Earth-Sun distance: r = 1.50 x 1011 m

An object weighs 432 N on the surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth’s surface, what is its weight?

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 friction after the crate is pushed 12.0 m if the coefficient of kinetic friction between the crate and the surface is 0.25.

A car of mass 1750 kg accelerates from 0.00 m/s to 35.0 m/s.  What was the net work done on the car? 

p2something.png An object slides a distance d = 9.00 m down an 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 and the coefficient of kinetic friction between the object and the surface is 0.25.