Question

1. a string of negligible mass is attached to a box of mass m. with the string taut, the box sits at rest on top of a scale, as shown. the scale has a force reading of $f_n$. derive the equation for the magnitude of the tension $f_t$ in the string.

Explanation:

Step1: Identify forces on the box

Forces: gravity $F_g = mg$ downward, normal force $F_N$ upward, tension $F_T$ upward.

Step2: Apply equilibrium condition

Since the box is at rest, net force is 0: $F_T + F_N = mg$

Step3: Solve for tension $F_T$

Rearrange the equilibrium equation to isolate $F_T$.
$F_T = mg - F_N$

Answer:

$F_T = mg - F_N$