1) A 500 kg mass is released at rest from a distance of two Earth radii above the surface of the Earth. Find the speed of the mass when it has fallen to a distance of one radius above the surface of the Earth.
2) If the mass of Jupiter is 1.8 x 10^27 kg and its radius is 7.1 x 10^7 m, then find the escape velocity for an object launched from the surface of Jupiter.
3) A person pushes with a force of 10.0 N on a stick pin to try to push it into a bulletin board. If the tip of the needle is a circle with a radius of 0.12 mm, then what is the average pressure (in Pascals) on the board at the tip of the pin?
4) An object has a volume of 0.25 m^3 and weighs 3000 N. What will be its apparent weight when submerged in water?