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You set out to prove to a friend skeptical of the benefits of exercise that running does in fact increase your longevity. One hot and humid summer day, while your friend takes a snooze in the shade under a tree, you run around the tree in the blazing sun at a steady 12 mph = 5.4 m/s for what is, according to your wristwatch, one hour.
(a) For how long are you running according to your friend?
(b) How far do you perceive yourself to have run?
(c) How far have you run according to your friend?
(d) How much time will you have added to your life because of time dilation?
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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