Two 64 kg stick figures are performing an extreme blob jump as shown in the diagram to the right
One stick figure stands atop a 7.0 m high platform with a 256 kg boulder. A second stick figure stands a partially inflated airbag known as a blob (or water trampoline). The first stick figure rolls the boulder off the edge of the platform. It falls onto the blob, catapulting the second stick figure into the air. What is the maximum height to which the second stick figure can rise? Assume that stick figures, boulders, and blobs obey the law of conservation of energy.

Ogle–2013–blg–0723 is an exoplanet that is similar to earth in size and proximity to its star. this exoplanet has mass m=4.18×1024kg and radius r=5.66×106m. an astronaut whose weight on earth is w=735n lands on the planet. a. calculate m, the mass of the astronaut. b. calculate gp? , the acceleration due to gravity on the surface of ogle–2013–blg–0723. c. calculate wp? , the weight of the astronaut on the surface of ogle–2013–blg–0723. d. calculate v, the minimum velocity required to put an object into orbit above ogle–2013–blg–0723. e. calculate t, the time required to complete an orbit around ogle–2013–blg–0723.

The law of conservation of energy states that energy cannot be created or , energy can be from one substance to another. the first blank is ' destroyed ' and for the second blank is ' transferred '

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.