A simple elevator ride can teach you quite a bit about the normal force as this

Question

A simple elevator ride can teach you quite a bit about the normal force as this rider below can (hopefully) tell you. There are three different scenarios given, detailing the riders experience in an unnamed hotel. For each scenario, calculate the normal force, FN,1-3, acting on the rider if his mass is m = 72.1 kg and the acceleration due to gravity g = 9.81 m/s2. In scenario 1, the elevator has constant velocity. In scenario 2 the elevator is moving with upward acceleration a2 = 4.84 m/s2. Finally, in scenario 3, unfortunately for the rider, the cable breaks and the elevator accelerates downward at a3 = 9.81 m/s2.

Explanation / Answer

for first case

there is no acceleration so normal force=mg=736.73 N

for second case

acceleration is upward

normal force(=N) is also upward

so N-mg=ma2

a2=4.84 m/s^2

N=m(g+a2)=1100.215 N

for third case

acceleration is downwards

and normal force(=N) is upwards

mg-N=ma3

a3=g

N=m(g-a3)=0

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