This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify all forces and their components. The point P is in equilibrium, meaning the net force in both the horizontal (x) and vertical (y) directions is zero. Let's define the positive x-direction as to the right and the positive y-direction as upwards. The forces acting on point P are: • A 2 N force acting at 45^ to the left of the vertical. • A 1 N force acting at 45^ to the right of the vertical. • Force F_1 acting horizontally to the right. • Force F_2 acting vertically downwards. We use (45^) = (1)/(sqrt(2)) and (45^) = (1)/(sqrt(2)). Step 2: Resolve forces into x-components. The sum of forces in the x-direction must be zero ( F_x = 0). • x-component of 2 N force: -2 (45^) (negative because it's to the left). • x-component of 1 N force: +1 (45^) (positive because it's to the right). • x-component of F_1: +F_1 (positive because it's to the right). • x-component of F_2: 0. F_x = -2 (45^) + 1 (45^) + F_1 = 0 -2 ((1)/(sqrt(2))) + 1 ((1)/(sqrt(2))) + F_1 = 0 -(2)/(sqrt(2)) + (1)/(sqrt(2)) + F_1 = 0 -(1)/(sqrt(2)) + F_1 = 0 F_1 = (1)/(sqrt(2)) N Step 3: Resolve forces into y-components. The sum of forces in the y-direction must be zero ( F_y = 0). • y-component of 2 N force: +2 (45^) (positive because it's upwards). • y-component of 1 N force: +1 (45^) (positive because it's upwards). • y-component of F_1: 0. • y-component of F_2: -F_2 (negative because it's downwards). F_y = 2 (45^) + 1 (45^) - F_2 = 0 2 ((1)/(sqrt(2))) + 1 ((1)/(sqrt(2))) - F_2 = 0 (2)/(sqrt(2)) + (1)/(sqrt(2)) - F_2 = 0 (3)/(sqrt(2)) - F_2 = 0 F_2 = (3)/(sqrt(2)) N Step 4: Compare with options. We found F_1 = (1)/(sqrt(2)) N and F_2 = (3)/(sqrt(2)) N. This matches option (a). The final answer is (a).