Question

question 20 (1 point)
a person of weight 480 n stands on a scale in an elevator. what will the scale be reading when the elevator is accelerating downward at 4.00 m/s2?
196 n
284 n
676 n
480 n

Explanation:

Step1: Find mass from weight

Weight \( W = mg \), so mass \( m=\frac{W}{g} \). Taking \( g = 9.8\ m/s^2 \) and \( W = 480\ N \), we get \( m=\frac{480}{9.8}\approx48.98\ kg \).

Step2: Apply Newton's second law

The forces on the person are weight \( W \) downward and normal force \( N \) (scale reading) upward. Acceleration \( a = 4.00\ m/s^2 \) downward. Using \( F_{net}=ma \), \( W - N = ma \). So \( N = W - ma \).
Substitute \( W = 480\ N \), \( m\approx48.98\ kg \), \( a = 4.00\ m/s^2 \):
\( N = 480 - 48.98\times4 = 480 - 195.92\approx284.08\ N \approx284\ N \).

Answer:

284 N (corresponding to the option: 284 N)