What is the kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s?
a. 12,000 j
b. 6,000 j
c. 2,940 j
d. 5,880 j

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Air initially at 0.75 bar, 1000 k, and occupying a volume of 0.12 m^3 undergoes two processes. process 1-2: the air is compressed isothermally until the volume is halved. process 2-3: the air undergoes a constant pressure process until the volume is halved again. assume ideal gas behavior. a) determine the mass of the air, in kg. b) the work and the heat transfer for each of the two processes, in kj. (100 kj = 1 bar . m^3)

Identify the correct relation showing that the radius r of the orbit of a moon of a given planet can be determined from the radius r of the planet, the acceleration of gravity at the surface of the planet, and the time τ required by the moon to complete one full revolution about the planet. determine the acceleration of gravity at the surface of the planet jupiter knowing that r = 71 492 km and that t= 3.551 days and r= 670.9 × 10^3 km for its moon europa.