Aparticle of charge q is fixed at the origin of an xy coordinate system. at t = 0 a particle (m = 0.754 g, q = 2.01 µc is located on the x axis at x = 24.3 cm, moving with a speed of 49.8 m/s in the positive y direction. for what value of q will the moving particle execute circular motion? (neglect the gravitational force on the particle.)

Oxygen undergoes an isentropic expansion from 120 degree c and 280 kpa absolute to 140 kpa absolute. determine the final temperature of the oxygen and the amount of work per kg of o_2 produced in the process if it is adiabatic.

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)

Steelhead trout migrate up stream to spawn. occasionally they need to leap up small waterfalls to continue their journey. fortunately, steelhead are remarkable jumpers, capable of leaving the water at a speed of 8.0 m/s. a. what is the maximum height a steelhead trout can jump? b. leaving the water at 8.0 m/s, the trout lands on top of the water fall 1.8 m high. how long was it in the air?