Question

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 ). which of the following must be a correct equation for the magnitude ( f_t ) of the tension in the string?
a ( f_t = f_n + mg )
b ( f_t = f_n )
c ( f_t = mg )
d ( f_t = mg - f_n )

Explanation:

Step1: Analyze the forces acting on the box

The box is at rest, so the net force on it is zero. The forces acting on the box are the gravitational force \(F_g = mg\) (downward), the normal force \(F_N\) (upward) from the scale, and the tension force \(F_T\) (upward) from the string.

Step2: Apply Newton's second law (\(F_{net}=0\))

Since \(F_{net}=0\), we have \(F_T + F_N - mg=0\).

Step3: Solve for \(F_T\)

Rearrange the equation \(F_T + F_N - mg = 0\) to get \(F_T=mg - F_N\).

Answer:

D. \(F_T = mg - F_N\)