h2. Part A
Suppose a person with a weight of 686 N is in an elevator which is descending at a constant rate of 1.0 m/s and speeding up at a rate of 3.0 m/s{color:black}^2^{color}. What is the person's apparent weight?
h4. Solution
{toggle-cloak:id=Asys} *System:* {cloak:id=Asys}Person as a [point particle].{cloak}
{toggle-cloak:id=Aint} *Interactions:* {cloak:id=Aint}External influences from the earth (gravity) and the floor of the elevator (normal force).{cloak}
{toggle-cloak:id=Amod} *Model:* {cloak:id=Amod}[Point Particle Dynamics].{cloak}
{toggle-cloak:id=Aapp} *Approach:*
{cloak:id=Aapp}
{toggle-cloak:id=AFBD} {color:red}*Diagrammatic Representations*{color}
{cloak:id=AFBD}The physical picture and free body diagram for the person is:
|!elevator1.gif!|!elevator2.gif!|
||Physical Picture||Free Body Diagram||
{cloak:AFBD}
{toggle-cloak:id=Amath} {color:red}*Mathematical Representation*{color}
{cloak:id=Amath}which leads to the form of [Newton's 2nd Law|Newton's Second Law] for the _y_ direction:
{latex}\begin{large}\[ \sum F_{y} = N - mg = ma_{y} \]\end{large}{latex}
In our coordinates, the acceleration of the person is _a_~y~ = -3.0 m/s{color:black}^2^{color}, giving:
{latex}\begin{large}\[ N = ma_{y} + mg = \mbox{476 N} \]\end{large}{latex}
{cloak:Amath}
{toggle-cloak:id=Acheck} {color:red}*Is the answer sensible?*{color}
{cloak:id=Acheck}
{tip}This result for the normal force is less than the person's usual weight, in agreement with our expectation that the person should feel lighter while accelerating downward.{tip}
{cloak:Acheck}
{cloak:Aapp}
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