Question

Four forces are acting on an object in static equilibrium: Force 1 has a magnitude of 46.0 N and is acting at an angle of (45 + A) degrees above the positive x-axis. Force 2 has a magnitude of (15+B) N and is acting along the positive x-axis. Force 3 has a magnitude of 34.5 N and is acting along the negative y-axis. Find the magnitude of the last force, F₄. Give your answer in newtons (N) and with 3 significant figures

A = 7 B = 13

Answer 1

From given data,  ; ;

Also given that and

Resolve the given forces into components

i) Horizontal component is  

  

ii) Vertical component is

  

  

i) horizontal component is

ii) vertical component is

  

i) Horizontal component is

ii) Vertical component is

Let us consider the horizontal and vertical components of force-4 as shown in the figure.

Thus at equilibrium,

i)Algebraic sum of horizontal component of forces is zero. That is

ii) Algebraic sum of vertical components of forces is zero. That is

Therefore, the magnitude of force F-4 is given by

  

  

Thus, the magnitude of force F-4 is