Question

a. to begin with, set the applied force to zero and set the weight of the box to be 10 n. if the box just sits there stationary, what is its acceleration? what does this mean about the magnitudes of the normal force and the weight of the box. b. now set the applied force to - 10n (this pushes down on the box with a force of 10 n). what total force is pushing/pulling the box down?

Explanation:

Step1: Determine acceleration for stationary box

According to Newton's first law, a stationary object has no change in velocity. Acceleration $a=\frac{\Delta v}{\Delta t}$, and since $\Delta v = 0$ for a stationary object, $a = 0$.

Step2: Analyze normal and weight force for stationary box

In the vertical - direction, for a stationary box on a flat surface with no applied vertical force other than weight, the net force $F_{net}=N - W=ma$. Since $a = 0$, then $N=W$. Here $W = 10\ N$, so $N = 10\ N$.

Step3: Calculate total downward force

The weight of the box acts downwards with a force $W = 10\ N$, and the applied force $F=- 10\ N$ also acts downwards. The total downward force $F_{down}=W + |F|$. Substituting the values, $F_{down}=10+10=20\ N$.

Answer:

a. Acceleration: $0\ m/s^{2}$, Normal force magnitude: $10\ N$ (equal to weight magnitude)
b. Total downward - force: $20\ N$