If a radioactive material has a half-life of 15 y what fraction of the material will remain after 30 y

Amodel rocket with a mass of 0.212 kg is launched into the air with an initial speed of 84 m/s. how much kinetic energy will the rocket have at a height of 214 m? assume there is no wind resistance. 634 j 303 j

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

Estimate the kinetic energy of mars with respect to the sun as the sum of two terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the sun. (assume mars is a uniform sphere with mass = 6.4×10 to the power of 23 kg, radius = 3.4×10 to the power of 6 m, rotation period = 24.7 hours, orbital period = 686 days and is 2.3×10 to the power of 8 km from the sun.)