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Electric winch pulley systems like the one shown below are often used to place equipment into the ocean from a research vessel (like the Scripps Oceanography ship Sally Ride). Assume the motors of one of these winches is powered a battery with an total energy capacity (potential energy) of E_{battery} =
E?battery ??=7.64 Watt-hour and total efficiency (fraction of stored energy turned into useful mechanical work) of ε = 0.252. The motor, fully charged, is connected to a cable through a pulley system to a CTD (conductivity, temperature and pressure/depth) instrument with a mass of 94.7 kg. If the CTD instrument, initially at rest, is pulled vertically up from the water, how high can it go before the motor battery is completed drained?
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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