Question

the apparent weight of a passenger in an elevator is greater than his true weight. which one of the following is true?
the elevator is either moving upward with a decreasing speed or moving downward with a decreasing speed.
the elevator is either moving upward with an increasing speed or moving downward with a decreasing speed.
the elevator is either moving upward with a decreasing speed or moving downward with an increasing speed.
the elevator is either moving upward with an increasing speed or moving upward with a decreasing speed.
the elevator is either moving upward with an increasing speed or moving downward with an increasing speed.

Explanation:

Step1: Recall Newton's second - law for elevator problem

Let the true weight of the passenger be $mg$ and the normal force on the passenger (which is the apparent weight) be $N$. According to Newton's second - law, $F_{net}=ma$, so $N - mg=ma$ (taking the upward direction as positive), then $N = m(g + a)$. When $N>mg$, it means $a>0$ (upward acceleration).

Step2: Analyze the motion of the elevator for upward and downward cases

• For upward motion: When the elevator is moving upward with an increasing speed, the acceleration $a>0$ (the velocity and acceleration are in the same direction).
• For downward motion: When the elevator is moving downward with a decreasing speed, the acceleration is upward ($a>0$) because the velocity is downward but the rate of change of velocity is in the opposite (upward) direction.

Answer:

The elevator is either moving upward with an increasing speed or moving downward with a decreasing speed.