Question

problem 7: you weigh yourself on a scale in an elevator at rest. your mass is m = 65 kg. what force does the scale read in newtons? now suppose that the elevator you are in is accelerating downward at a = 0.6 m/s². what does the scale read in newtons? do not forget the free body diagram and newton’s second - law equation.

Explanation:

Step1: Find the force when elevator is at rest

When the elevator is at rest, the normal force $N$ (the force the scale reads) is equal to the weight of the person. According to Newton's second - law $F = ma$, and since $a = 0$, $N=mg$. The acceleration due to gravity $g = 9.8\ m/s^{2}$ and $m = 65\ kg$. So $N_1=mg=65\times9.8 = 637\ N$.

Step2: Analyze the situation when elevator is accelerating downward

Draw a free - body diagram. The forces acting on the person are the force of gravity $mg$ (downward) and the normal force $N$ (upward). According to Newton's second law $F_{net}=ma$, and taking downwards as positive, $mg - N_2=ma$. We can re - arrange the equation to solve for $N_2$: $N_2=m(g - a)$. Substitute $m = 65\ kg$, $g = 9.8\ m/s^{2}$ and $a = 0.6\ m/s^{2}$ into the equation. Then $N_2=65\times(9.8 - 0.6)=65\times9.2=598\ N$.

Answer:

When the elevator is at rest, the scale reads 637 N. When the elevator is accelerating downward at $0.6\ m/s^{2}$, the scale reads 598 N.