Solving Elevator Force Problem: Acceleration Calculation & Direction Explanation

[psycovic23]

The question reads "A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only .75 of the person's regular weight. Calculate the acceleration of the elevator, and the direction."

I know that the direction is going down because..it just seems like common sense, and I know the answer is 2.5m/s^2, but I don't understand how that was reached...any help? Thank you.

 

[assyrian_77]

Net sum of forces has to be constant. Taking 'up' as the positive direction, we can write:

N-ma=mg,

where a is the acceleration and N the normal force. The scale shows the normal force. Thus, N=0.75mg and we can write

0.75mg-ma=mg => a=-0.25*g=-2.45 m/s^2 (9.8 m/s^2)

Thus, acceleration is 2.45 in the negative direction, i.e. down.

 

[hypermorphism]

Good intuition on the direction. Consider that a reading of the person's weight is a reading of the force the person is exerting on the scale. In other words, 1.00*mg if the person is only under the force of Earth's gravity near sea level. Therefore, the net vertical force on the person right now is 0.75*mg.

 

[psycovic23]

Ah, thank you very much! I guess I was looking at the wrong thing..I was trying to figure out the forces of the elevator, not the person standing on the scale.