Consider a giant molecular cloud (gmc) which has typical temperature and number density in its dense core of t = 10 k and n = 1010 m−3 . note that dense clouds are predominantly molecular hydrogen so that n = nh2 and rho0 = 2mhnh2 = 3 × 10−17 kg m−3 . calculate the jeans mass and jeans length for the gmc. note: you will need to estimate µ.

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm

Aphase diagram assumes is kept constant.