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: Resolve the forces into their x and y components. We are given the following values from question 40: (53^) = (37^) = 0.8 and (53^) = (37^) = 0.6. Let North be the positive y-axis and East be the positive x-axis. For force F_1 = 75 \, N at 53^ west of north: The angle with the positive y-axis towards the negative x-axis is 53^. The x-component is negative, and the y-component is positive. F_1x = -F_1 (53^) = -75 \, N × 0.8 = -60 \, N F_1y = F_1 (53^) = 75 \, N × 0.6 = 45 \, N For force F_2 = 100 \, N at 37^ east of north: The angle with the positive y-axis towards the positive x-axis is 37^. The x-component is positive, and the y-component is positive. F_2x = F_2 (37^) = 100 \, N × 0.6 = 60 \, N F_2y = F_2 (37^) = 100 \, N × 0.8 = 80 \, N Step 2: Calculate the components of the resultant force. The resultant force R has components R_x and R_y: R_x = F_1x + F_2x = -60 \, N + 60 \, N = 0 \, N R_y = F_1y + F_2y = 45 \, N + 80 \, N = 125 \, N Step 3: Determine the magnitude and direction of the resultant force. The magnitude of the resultant force is: |R| = sqrt(R_x^2 + R_y^2) = sqrt((0 \, N))^2 + (125 \, N)^2 = sqrt(15625 \, N)^2 = 125 \, N Since R_x = 0 and R_y is positive, the resultant force is directed purely along the positive y-axis, which corresponds to North. Step 4: Apply the graphical scale to find the length of the arrow line. The given graphical scale is 1 \, cm for 10 \, N force. Length of the arrow line = Magnitude of resultant forceForce per cm Length = 125 \, N10 \, N/cm = 12.5 \, cm The possible length of the arrow line is 12.5 \, cm and its direction is North. Comparing this with the given options: A. 12.5 \, cm to the North B. 17.3 \, cm to 45^ North of East C. 1.25 \, cm to the North D. 1.73 \, cm to 45^ North of East The calculated result matches option A. The final answer is A. 12.5 \, cm to the North. Send me the next one 📸