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
To find the magnitude of the resultant force, we use the Law of Cosines for forces. Step 1: Identify the given magnitudes of the forces and the angle between them. Let F_1 = 7 \, N Let F_2 = 4 \, N Let = 120^ Step 2: Apply the formula for the magnitude of the resultant force (R). The formula is: R = sqrt(F_1^2 + F_2^2 + 2F_1F_2 ) Step 3: Substitute the given values into the formula. R = sqrt((7 \, N))^2 + (4 \, N)^2 + 2(7 \, N)(4 \, N) (120^) Step 4: Calculate the square of the forces and the cosine of the angle. We know that (120^) = -(1)/(2). R = sqrt(49 \, N)^2 + 16 \, N^2 + 2(28 \, N^2) (-(1)/(2)) Step 5: Perform the arithmetic operations. R = sqrt(49 \, N)^2 + 16 \, N^2 - 28 \, N^2 R = sqrt(65 \, N)^2 - 28 \, N^2 R = sqrt(37 \, N)^2 Step 6: Calculate the final magnitude. R = sqrt(37) \, N The magnitude of their resultant is sqrt(37) \, N. 3 done, 2 left today. You're making progress.