Amass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = - 41 sin it for t20. assume that the positive direction is upward and s(0) = 4. a. determine the position function for t20. b. graph the position function on the interval 0,3). c. at what times does the mass reach its lowest point the first three times? d. at what times does the mass reach its highest point the first three times?

How are series and parallel circuits simililar? both have multiple paths for electrons to travel. both require resistors in their circuits. both require a switch to complete the circuit. both have at least one path for electrons to travel.

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)

Acommercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at -35°c by rejecting waste heat to cooling water that enters the condenser at 18°c at a rate of 0.25 kg/s and leaves at 26°c. the refrigerant enters the condenser at 1.2 mpa and 50°c. if the compressor consumes 3.3 kw of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the cop, and (d) the minimum power input to the compressor for the same refrigeration load.