I need help with this questions

Question

1.) A force of 20 N acts towards the west. Another force acts at the same point so that the resultant of the two forces is zero. What is the magnitude and direction of the second force?

2.) A force of 20 N acts towards the east. Another force of 27 N acts at the same point towards the west. What is the magnitude and direction of a third force that produces a resultant of 10 N toward the east.

Thank you :)

Answer 1

Hey Patrick,

1) For two forces to cancel, one must be equal and opposite to the other. This means that the magnitude is exactly the same and the direction is exactly opposite. So in this example, it would be 20N to the east.

2) Here it will help to call one direction positive and the other negative, so we can just write it mathematically. I'll call East positive

1. Resultant = F_net = +10N
2. F_net = 20N - 27N + F₃
3. 10N = 20N - 27N + F₃
4. Just solve this expression for F₃. Then use your +/- choice to go back to direction. So a negative value would be West, positive will be east.