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: Calculate the weight of the body. The mass of the body is m = 2.5 kg. The acceleration due to gravity is g = 10 ms^-2. The weight of the body, W, is given by W = mg. W = 2.5 kg × 10 ms^-2 = 25 N Step 2: Identify the forces and angles for Lami's Theorem. Let T_1 be the tension in string XP and T_2 be the tension in string YP. The body is in equilibrium under the action of three forces: T_1, T_2, and its weight W. The angles are given with respect to the downward vertical. • The angle between T_1 and the downward vertical is 40^. • The angle between T_2 and the downward vertical is 50^. For Lami's Theorem, we need the angles between the forces. • The angle between T_1 and W is 40^. • The angle between T_2 and W is 50^. • The angle between T_1 and T_2 is the sum of their angles from the vertical, which is 40^ + 50^ = 90^. Step 3: Apply Lami's Theorem. Lami's Theorem states that for three forces in equilibrium, each force is proportional to the sine of the angle between the other two forces. (T_1)/((angle between ) T_2 and W) = (T_2)/((angle between ) T_1 and W) = (W)/((angle between ) T_1 and T_2) Substituting the values: (T_1)/((50^)) = (T_2)/((40^)) = 25 N(90^) Since (90^) = 1: (T_1)/((50^)) = (T_2)/((40^)) = 25 N Step 4: Solve for the tensions T_1 and T_2. From the equations: T_1 = 25 (50^) T_2 = 25 (40^) Using approximate values for sine: (50^) ≈ 0.7660 and (40^) ≈ 0.6428. T_1 = 25 × 0.7660 = 19.15 N T_2 = 25 × 0.6428 = 16.07 N Rounding to three significant figures: T_1 ≈ 19.2 N T_2 ≈ 16.1 N The tensions in the strings are: T_1 ≈ 19.2 N, T_2 ≈ 16.1 N Last free one today — make it count tomorrow, or type /upgrade for unlimited.