An object of mass 5 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground?
The given values are
The equation of motion is role="math" localid="1664170601861"
Put all the given values
Hence the equation of motion is role="math" localid="1664170624317"
Hence, the object will strike the ground in 1019 sec.
An object at rest on an inclined plane will not slide until the component of the gravitational force down the incline is sufficient to overcome the force due to static friction. Static friction is governed by an experimental law somewhat like that of kinetic friction (Problem 18); it has a magnitude of at most N, where m is the coefficient of static friction and N is, again, the magnitude of the normal force exerted by the surface on the object. If the plane is inclined at an angle a, determine the critical value 0 for which the object will slide if o but will not move for o.
On a hot Saturday morning while people are working inside, the air conditioner keeps the temperature inside the building at . At noon the air conditioner is turned off, and the people go home. The temperature outside is a constant for the rest of the afternoon. If the time constant for the building is 4 hr, what will be the temperature inside the building at 2:00 p.m.? At 6:00 p.m.? When will the temperature inside the building reach ?
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