Given a sphere with radius r, find the height of a pyramid of minimum volume whose base is a square and whose base and triangula
r faces are all tangent to the sphere. What if the base of the pyramid is a regular n-gon? (A regular n-gon is a polygon with n equal sides and angles.) (Use the fact that the volume of a pyramid is V = 1 3Ah, where A is the area of the base.)
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Answer:
Under the reasonable assumption that the brick has more mass than the feather, the brick experiences a greater force of air friction.
Explanation:
<u>Objects at terminal velocity</u>, only under the influence of gravity, have maximized their speed and <u>have an acceleration of zero</u>. Thus, neither object is accelerating.
Recall Newton's second law:
Since acceleration for each object is zero, the sum of the force acting on each of those objects must also be zero.
Since the only forces acting on the objects are gravity and the force of air friction, in order to zero out, <u>the force of air friction must be equal in magnitude and opposite in direction to the force of gravity</u>.
Recall that near the surface of the earth, , so <u>the Force of Gravity acting on an object is directly proportional to the object's mass</u>. <em>(A similar argument could be made even if this were not taking place on the surface of the earth, so long as the objects were the same distance from the object providing gravitational influence).</em>
If the masses of the objects are different, <u>the object with the greater mass will experience</u> a larger force of gravity, and hence <u>a larger force of air friction</u> at terminal velocity.
Under the reasonable assumption that the brick has more mass than the feather, the brick experiences a greater force of air friction.