Afew years ago, serena williams dived to hit a tennis ball right after it bounced off the ground. the ball bounced on the ground 11.5 m from the net, and after serena hit the ball it flew over the 0.950 m high net and bounced in her opponent's court about 1.05 s after she hit it. if there had been no gravity, the ball would have been 1.73 m higher than the net when it crossed over.. how fast was the ball moving when it left serena\'s racket? ignore any effects from ball spin and air resistance.

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)