Question

fill in the missing force to make each statement true. show your work in the box provided. 1. the box will move to the right with a force of 50 n. 2. the box will not move.

Explanation:

Step1: Analyze forces for right - moving box

Let the missing force be $F$. The net force to the right is given as $50$ N. Forces to the right are $F + 25$ N and force to the left is $50$ N. Using net - force formula $F_{net}=F_{right}-F_{left}$, we have $50=(F + 25)-50$.

Step2: Solve for $F$

Add $50$ to both sides of the equation: $50 + 50=F + 25$. Then $100=F + 25$. Subtract $25$ from both sides: $F=100 - 25=75$ N.

Step3: Analyze forces for non - moving box

For the box not to move, the net force must be zero. Let the missing force be $F$. Forces to the right are $75+F$ and force to the left is $125$ N. So, $75+F-125 = 0$.

Step4: Solve for $F$

First, simplify the left - hand side of the equation: $F-50 = 0$. Then add $50$ to both sides to get $F = 50$ N.

Answer:

1. $75$ N
2. $50$ N