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 rider\'s experience in an unnamed hotel. For each scenario, calculate the normal force, FN,1-3, acting on the rider if his mass is m = 76.6 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.

FN1=
FN2=
FN3=

Answer 1

1) 751.446N

2) 1122.19N

3) 0N

Step-by-step explanation:

When an object is inside an elevator it is subjected to two forces. These forces are the weight W of the object and the normal reaction
`F_N` of the floor of the elevator on the object.

Scenario 1: If the elevator is ascending or descending at a constant velocity, there will not be any unbalanced force acting on the object. In such case the weight of the object is equal to the normal reaction of the floor of the elevator.

`F_N=W.............(1)`

Recall that W = mg where g is acceleration due to gravity and m is the mass of the object. Hence in case 1, the normal force is given by

`F_(N1)=76.6*9.81\\F_(N1)=751.446N`

Scenario 2: If the elevator is ascending or moving upward with an acceleration a, there will be an unbalanced force F acting the object. This unbalanced force is the difference between the normal reaction force and the weight of the object.

`F=F_N-W..................(2)`

Therefore;

`F_N=F+W..................(3)`

Recall that F = ma, so we can write the following;

`F_N=ma+mg\\F_N=m(a+g)...................(4)`

Given;

`a=4.84m/s^2`.

Hence the normal force in case 2 is obtained as follows;

`F_(N2)=76.6(4.84+9.81)\\F_(N2)=76.6(14.65)\\F_(N2)=1122.19N`

Scenario 3: If the cable of the elevator breaks and it falls freely under gravity together with the object, there will be no contact between the object and the floor of the elevator. Therefore there will be no normal reaction force acting on the object.

`F_(N3)=0N`