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Chapter 6: Q. 66 (page 157)
A skater is gliding across frictionless ice at . Air resistance is not negligible. You can model the skater as a -tall,-diameter cylinder. What is the skater's speed later?
Speed of the skater afterSec is
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Very small objects, such as dust particles, experience a linear drag force,(bv, direction opposite the motion), where is a constant. That is, the quadratic model of drag of Equation fails for very small particles. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the gas.
a. Find an expression for the terminal speedof a spherical particle of radius and mass falling through a gas of viscosity .
b. Suppose a gust of wind has carrieda -diameter dust particle to a height of . If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density ofrole="math" localid="1647776411884" the viscosity ofair is , and you can assume that the falling dust particle reaches terminal speed almost instantly.
A rubber-wheeled cart rolls down a concrete incline. What is the cart鈥檚 acceleration if rolling friction is
(a) neglected and
(b) included?
Astronauts in space "weigh" themselves by oscillating on a CALC spring. Suppose the position of an oscillating astronaut is given by, where is in . What force does the spring exert on the astronaut at
(a) and
(b) ? Note that the angle of the sine function is in radians.
A kg wood block is launched up a wooden ramp that is inclined at a angle. The block鈥檚 initial speed is m/s.
a. What vertical height does the block reach above its starting point?
b. What speed does it have when it slides back down to its starting point?
A wood block is pressed against a vertical wood wall by theforce shown in . If the block is initially at rest, will it move upward, move downward, or stay at rest?
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