An elevator accelerates upward in 3.40 s to a final speed of 7.40 m/s.

Question

 An elevator accelerates upward in 3.40 s to a final speed of 7.40 m/s. A 56.0 kg person is standing on a bathroom scale in the elevator. Determine the apparent weight of the passenger.

Answer 1

By definition the apparent weight, P, - is the force that the body produces on a surface or a scale. This force is applied to the surface or scale from the body. The force that the scale or surface produces on the body - is normal reaction force N. With accordance to Newtons third law those two forces are opposite in directions, but same in magnitude. Hence, we will be finding normal reaction force that acts on the body up, but has the same magnitude that the apparent weight. Usually on the diagram we show all forces that acts on the body. The second force that acts on the body in this case is weight W = mg directed down and exerted from the Earth on the body.

Please keep in mind that weight is a gravitational force and at a given location is not changing. Apparent weight is electromagnetic in its nature and could vary.

Now we can write the Newtons second law

N + mg = ma - vector form!

Because the acceleration is directed upward, we can write in scalar form

N - mg = ma

From here

N = m (g + a)

Acceleration could be found from kinematics formula

a = v /t

So for normal force we have

N = m (g + v/t)

But the apparent weight has the same magnitude, so we can write

P = m (g + v/t)

To find the numeric value of apparent weight you just plug in the values of mass, velocity and acceleration of the person.

You can see that if the acceleration of the body is upward, its apparent weight in magnitude is greater than weight of the body.