A small projectile is launched parallel to the ground at height with sufficient speed to orbit a completely smooth, airless planet. A bug rides inside a small hole inside the projectile. Is the bug weightless? Explain.
Yes. the bug is weightless because the bug is moving in the same direction as a projectile.
height of the projectile
speed of projectile to orbit a completely smooth, airless planet.
A bug rides inside a small hole inside the projectile.
Weightless - the feeling of there being no force between a bug and the space ship because both bug and it are accelerating downwards at the same value (when you fall, you are falling in the same direction in which gravity is pointing). Bug is 'weightless' although it has the same weight as it started out with -- moving in the same direction as the projectile.
If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola described by the equation
Hint: Each particle of water on the surface is subject to only two forces: gravity and the normal force due to the water underneath it. The normal force, as always, acts perpendicular to the surface.
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