165- A person of mass $80\ \text{kg}$ is inside an elevator. At the moment the elevator begins moving downward with constant acceleration $2\ \dfrac{\text{m}}{\text{s}^2}$, how many Newtons of force does the person exert on the elevator?
$$\left(g = 10\ \frac{\text{m}}{\text{s}^2}\right)$$

• [(1)] $960$ (2) $800$ (3) $160$ (4) $640$

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Workspace for Calculations
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163. A scale is fixed to the floor of an elevator. During motion, the scale shows a person's weight greater than the rest value. How is the elevator moving?

• [(1)] Necessarily accelerating upward
• [(2)] Necessarily accelerating downward
• [(3)] Accelerating upward or decelerating downward
• [(4)] Decelerating upward or accelerating downward

A block of mass $M$ placed inside a box descends vertically with acceleration $a$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of $|a|$ will be
(1) $g$
(2) $\frac{3g}{4}$
(3) $\frac{g}{2}$
(4) $\frac{g}{4}$