13. A force of 20 N at angle of 30^circ to the horizontal and a force F_(2) at an angle of 60^circ to the horizontal are applied on an object as shown in the Figure below so as to make the object in equilibrium. Calculate the magnitude of the force F_(2) and weight of the object. square

To solve this problem, we will use the principles of static equilibrium, which state that the sum of all forces in any direction must be zero for an object to be in equilibrium. We have two forces, and , acting at angles to the horizontal, and the weight acting vertically downward.Given:- N at an angle of to the horizontal- is unknown, at an angle of to the horizontal- The weight is also unknownWe will resolve the forces into their horizontal (x-axis) and vertical (y-axis) components and then apply the equilibrium conditions.Step 1: Resolve into horizontal and vertical components.- The horizontal component of is \(F_{1x} = F_1 \cos(30^\circ)\)- The vertical component of is \(F_{1y} = F_1 \sin(30^\circ)\)Step 2: Resolve into horizontal and vertical components.- The horizontal component of is \(F_{2x} = F_2 \cos(60^\circ)\)- The vertical component of is \(F_{2y} = F_2 \sin(60^\circ)\)Step 3: Apply the equilibrium condition for the horizontal direction.Since the object is in equilibrium, the sum of the horizontal forces must be zero: Step 4: Apply the equilibrium condition for the vertical direction.The sum of the vertical forces must also be zero: Now let's calculate the components and solve for and .\(F_{1x} = 20 \cos(30^\circ) = 20 \times \frac{\sqrt{3}}{2} = 10\sqrt{3}\) N\(F_{1y} = 20 \sin(30^\circ) = 20 \times \frac{1}{2} = 10\) NFrom Step 3, we have:\(10\sqrt{3} - F_2 \cos(60^\circ) = 0\)\(F_2 \cos(60^\circ) = 10\sqrt{3}\)Since \(\cos(60^\circ) = \frac{1}{2}\), we can solve for : NFrom Step 4, we have:\(10 + F_2 \sin(60^\circ) - W = 0\)Substitute into the equation:\(10 + (20\sqrt{3}) \sin(60^\circ) - W = 0\)Since \(\sin(60^\circ) = \frac{\sqrt{3}}{2}\), we can solve for : NFinal Answer:- The magnitude of the force is N.- The weight of the object is N.