Spring scales work by measuring the displacement of a spring that supports both the platform of mass mp and the object, of mass m, whose weight is being measured. Most scales read zero when no mass m has been placed on them; that is, they are calibrated so that the weight reading accounts for the mass of the platform mp. Assume that the spring is linear elastic with spring constant k.

Required:
If the mass m is gently placed on the spring scale (it is released from zero height above the scale), determine the maximum reading on the scale after the mass is released.

Determine the age of a fossil if it had only one eighth of its original carbon-14 content remaining?

Because air contracts as it cools, the air pressure inside a freezer is typically lower than on the outside. why do ice cubes inside a freezer tend to shrink over time? a. the ice dissolves oxygen from the air, forming a denser crystalline matrix.b. the ice reacts chemically with carbon dioxide in the air, forming gaseous carbon compounds.c. the ice melts, and then the liquid freezes as ice crystals on the bottom of the freezer.d. the ice sublimes, and then the water vapor deposits as ice crystals on the sides of the freezer.

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)