Answer to Question #256327 in Physics for Jhon

Question

3. Two forces of 40.0 N and 30.0 N act on a particle. a) Find the maximum and minimum magnitudes of the resultant of these two forces. b) What is the magnitude of the resultant if the angle between them is 45ᵒ?

Answer 1

a) The maximum is

$$D_\text{max}=30+40=70\text{ N}.$$

The minimum is

$$D_\text{min}=|30-40|=10\text{ N}.$$

b) The resultant is

$$D=\sqrt{30^2+40^2-2·30·40\cos(90°+45°)}=\\ =64.8\text{ N}.$$