Use this scenario to answer the four following questions. a person is on a sled on top of a snow covered hill. the vertical distance from the top of the hill to the bottom is 12 meters. the sled and the person riding it have a combined mass of 60 kg. to start, person is pushed. the initial velocity is 1 m/s. at the bottom of the hill, the sled and the person have a velocity of 10 m/s. use g=9.8 m/s2 or g=10 m/s2 for the gravitational acceleration. what is the initial total mechanical energy of the person and their sled?

Apulley system lifts a 500-ib block 1.0 foot with an effort of only 50 ib. if the 50 ib moves 30 feet, calculate the efficiency of the pulley system. a. 30% b. 33% c. 70% d. 67%

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)

Aball horizontally thrown from a cliff at 8m/s