A plastic tube allows a flow of 12.7 cm3 /s of
water through it.
How long will it take to fill a 239 cm3
bottle
with water?
Answer in units of s.

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)

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

Awheel of mass 48 kg is lifted to a height of 0.8 m. how much gravitational potential energy is added to the wheel? acceleration due to gravity is g = 9.8 m/s2. a. 30.4 j b. 3.1 j c. 297.9 j d. 11,321 j