A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length.

a] In terms of U0, how much energy does it store when it is compressed twice as much? Uel/U0 =?

b] In terms of U0, how much energy does it store when it is compressed half as much? Uel/U0 = ?

c] In terms of x0, how much must it be compressed from its uncompressed length to store twice as much energy? x/x0 = ?

d] In terms of x0, how much must it be compressed from its uncompressed length to store half as much energy? x/x0 = ?

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)

Achild has maximum walking speed of 1.6 m/s. what is the length of the child's legs? 0.26 m

Macy always thought there were only a few hair colors blonde brown and black however when she actually began looking around she saw varying shades of these hair color what is a possible reason for so many different hair colors