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Q1. A 1.25x106 kg deep space exploration ship sits motionless in deep space studying a far off star. The crew decide to launch a 500 kg probe towards the star. The probe leaves the ship with a velocity of 1,200 m/s towards the star.
a. What velocity does the ship have after the launch of the probe?
b. Assuming the ship's engines can produce a force of 3.67x105 N, how long must they fire to bring the ship back to motionlessness (i.e. to a complete stop)?
Q2. To store the energy produced in 1hour by a 110 electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Suppose the upper reservoir is 510 meters above the lower one, and we can neglect the small change in depths of each. Water has a mass of for every 1000 kg per 1.03 cubic meters.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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