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
Fresh day Daniel, let's solve. To find the reaction at pivot X, we will use the principle of moments. For the plank to be in equilibrium, the sum of clockwise moments about any point must equal the sum of anti-clockwise moments about the same point. Step 1: Identify the given values and convert units. The length of the plank L = 3.00 m. The weight of the plank W = 44.0 N. Since the plank is uniform, its weight acts at its center, which is at (L)/(2) = 3.00 m2 = 1.50 m from either end. Pivot Y is 30.0 cm = 0.30 m from the left end. Pivot X is 50.0 cm = 0.50 m from the right end. Step 2: Choose a pivot point to calculate moments. To find the reaction force at X (R_X), we take moments about pivot Y. This eliminates the reaction force at Y (R_Y) from the equation. Step 3: Calculate the distances of the forces from pivot Y. • Distance of the plank's weight (W) from Y: The center of the plank is at 1.50 m from the left end. Pivot Y is at 0.30 m from the left end. d_W = 1.50 m - 0.30 m = 1.20 m This weight creates a clockwise moment about Y. • Distance of the reaction force at X (R_X) from Y: The total length of the plank is 3.00 m. The distance from the left end to Y is 0.30 m. The distance from the right end to X is 0.50 m. The distance between Y and X is: d_X = L - (distance from left end to Y) - (distance from right end to X) d_X = 3.00 m - 0.30 m - 0.50 m = 2.20 m This reaction force creates an anti-clockwise moment about Y. Step 4: Apply the principle of moments. Sum of clockwise moments = Sum of anti-clockwise moments W × d_W = R_X × d_X Substitute the known values: 44.0 N × 1.20 m = R_X × 2.20 m 52.8 N·m = R_X × 2.20 m Step 5: Solve for R_X. R_X = 52.8 N·m2.20 m R_X = 24.0 N Comparing this result with the given options: A. 40.5 N B. 24.0 N C. 20.0 N D. 16.2 N The calculated reaction at X matches option B. The final answer is B. 24.0 N. What's next? Send 'em!