Question

q 9. ===see the free body diagram below. given: total net force will sum to 18 newtons east. ===what force, if added to the diagram, will make the forces sum to 18 newtons east? given: net force = 18 n east. what force is needed to sum to 18 n east? missing force = ?

Explanation:

Step1: Analyze forces in North - South direction

Forces in North - South direction: \(9N\) North and \(9N\) South. Their resultant is \(9N - 9N=0N\) (since they are in opposite directions). So, the net force in the North - South direction is \(0N\).

Step2: Analyze forces in East - West direction

Let the missing force in the East - West direction be \(F\). We know that the net force in the East - West direction (since net force of the whole system is \(18N\) East and net force in North - South is \(0N\)) should be \(18N\) East.
We have a \(15N\) East force. Let the missing force be \(F\). Using the formula for the sum of forces in one - dimension (\(F_{net}=F_1 + F_2\)), where \(F_{net}=18N\) (East, positive direction) and \(F_1 = 15N\) (East, positive direction).
\(18N=15N+F\)

Step3: Solve for the missing force

Subtract \(15N\) from both sides of the equation \(18N=15N+F\).
\(F=18N - 15N\)
\(F = 3N\) East

Answer:

3 NEWTONS EAST