There is strong evidence that europa, a satellite of jupiter, has a liquid ocean beneath its icy surface. many scientists think we should land a vehicle there to search for life. before launching it, we would want to test such a lander under the gravity conditions at the surface of europa. one way to do this is to put the lander at the end of a rotating arm in an orbiting earth satellite.
if the arm is 6.00 m long and pivots about one end, at what angular speed (in rpm) should it spin so that the acceleration of the lander is the same as the acceleration due to gravity at the surface of europa? the mass of europa is 4.8x10^22 kg and its diameter is 3138 km .

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c. what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j. b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

Aspecified volume of space contains an electric field for which the magnitude is given by e=e0cos(ωt). suppose that e0 = 20 v/m and ω = 1.0 × 107 s−1. part a what is the maximum displacement current through a 0.80 m2 cross-sectional area of this volume? express your answer with the appropriate units. idisp, max i d i s p , m a x = nothing nothing request answer part b how would this area have to be oriented relative to the electric field to get this maximum displacement current?