A ball of mass 500 g hangs from a spring whose stiffness is 125 newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless 8cm from it's original position. In this situation the spring is stretched, and its length is 15 cm. What would be the relaxed length of the spring, if it were detached from the ball and laid on a table?

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)

Both independent and dependent clauses