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The Gravitron single-car roller coaster consists of a singleloop-the-loop. The car is initially pushed, giving it just theright mechanical energy so the riders on the coaster will feel"weightless" when they pass through the top of the circular arc. How heavy will they feel when they pass through the bottom of thearc (that is, what is the normal force pressing up on them whenthey are at the bottom of the loop)? Express the answer as amultiple of mg (their actual weight). Assume any effectsof friction or of air resistance are negligible.
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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