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
You're on a roll — Here's the solution for the resultant force: Step 1: Define the two forces and resolve them into components. Let F_1 be the horizontal force of 8 N. Let F_2 be the force of 5 N inclined at 45^ to the horizontal. For F_1: Since it's a horizontal force, its components are: F_1x = 8 N F_1y = 0 N For F_2: The force is 5 N at 45^ to the horizontal. F_2x = 5 (45^) = 5 × sqrt(2)2 ≈ 5 × 0.7071 = 3.5355 N F_2y = 5 (45^) = 5 × sqrt(2)2 ≈ 5 × 0.7071 = 3.5355 N Step 2: Sum the x-components and y-components to find the resultant force components. Let the resultant force be F_R. Total x-component (F_x): F_x = F_1x + F_2x = 8 N + 3.5355 N = 11.5355 N Total y-component (F_y): F_y = F_1y + F_2y = 0 N + 3.5355 N = 3.5355 N Step 3: Calculate the magnitude of the resultant force. The magnitude of the resultant force, |F_R|, is found using the Pythagorean theorem: |F_R| = sqrt(F_x^2 + F_y^2) |F_R| = sqrt((11.5355 N))^2 + (3.5355 N)^2 |F_R| = sqrt(133.067 + 12.500) |F_R| = sqrt(145.567) |F_R| ≈ 12.065 N Step 4: Calculate the direction of the resultant force. The direction is found using the arctangent function, measured from the horizontal axis: = ((F_y)/(F_x)) = (3.5355 N11.5355 N) = (0.3065) ≈ 17.03^ Since both F_x and F_y are positive, the direction is 17.03^ above the horizontal. The magnitude of the resultant force is 12.07 N and its direction is 17.03^ above the horizontal. That's 4 down. 1 left today — send the next one.