Question

question 19 (1 point)
person on a scale rides in an elevator. if the mass of the person is 60.0 kg and the elevator accelerates upward with an acceleration of 4.90 m/s2, what is the reading on the scale?
147 n
294 n
588 n
882 n

Explanation:

Step1: Identify the forces and acceleration

The scale reading is the normal force \( F_N \) exerted on the person. The person has mass \( m = 60.0 \, \text{kg} \), acceleration due to gravity \( g = 9.80 \, \text{m/s}^2 \), and upward acceleration \( a = 4.90 \, \text{m/s}^2 \). Using Newton's second law \( F_{\text{net}} = ma \), the net force is \( F_N - mg = ma \) (since upward is positive, normal force is upward, weight \( mg \) is downward).

Step2: Solve for normal force

Rearrange the equation: \( F_N = m(g + a) \). Substitute \( m = 60.0 \, \text{kg} \), \( g = 9.80 \, \text{m/s}^2 \), \( a = 4.90 \, \text{m/s}^2 \).
First, calculate \( g + a = 9.80 + 4.90 = 14.7 \, \text{m/s}^2 \).
Then, \( F_N = 60.0 \times 14.7 = 882 \, \text{N} \)? Wait, no, wait: Wait, no, wait, let's recalculate. Wait, \( 60 \times 14.7 \): \( 60 \times 10 = 600 \), \( 60 \times 4.7 = 282 \), total \( 882 \)? Wait, but wait, maybe I made a mistake. Wait, no, the formula is \( F_N = m(g + a) \) when accelerating upward. Wait, \( g = 9.8 \), \( a = 4.9 \), so \( g + a = 14.7 \). Then \( 60 \times 14.7 = 882 \). Wait, but let's check again. Wait, the options include 882 N. Wait, but let's verify the steps.

Wait, Newton's second law: the net force on the person is \( F_N - mg = ma \), so \( F_N = m(a + g) \). Plugging in the numbers: \( m = 60 \), \( a = 4.9 \), \( g = 9.8 \). So \( a + g = 14.7 \), \( 60 \times 14.7 = 882 \). So the scale reading is 882 N.

Answer:

882 N (corresponding to the option with 882 N)