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
eda, let's knock this out. Step 1: Calculate the work done. The work done W by a constant force F causing a displacement s is given by the dot product of the force and displacement vectors. W = F · s Given F = (5i + 2j - 3k)\, N and s = (2i + 3j + 4k)\, m. W = (5)(2) + (2)(3) + (-3)(4) W = 10 + 6 - 12 W = 4\, J The work done by the force is 4 J. Step 2: Calculate the magnitude of the force vector. |F| = sqrt(F_x^2 + F_y^2 + F_z^2) |F| = sqrt(5^2 + 2^2 + (-3)^2) |F| = sqrt(25 + 4 + 9) |F| = sqrt(38)\, N Step 3: Calculate the magnitude of the displacement vector. |s| = sqrt(s_x^2 + s_y^2 + s_z^2) |s| = sqrt(2^2 + 3^2 + 4^2) |s| = sqrt(4 + 9 + 16) |s| = sqrt(29)\, m Step 4: Calculate the angle between the force and displacement. The angle between two vectors can be found using the formula: = F · s|F| |s| We already found F · s = 4\, J. = (4)/(sqrt(38) · 29) = (4)/(sqrt(38 × 29)) = (4)/(sqrt(1102)) ≈ (4)/(33.196) ≈ 0.12049 = (0.12049) ≈ 83.08^ The angle between the force and displacement is 83.08^. Send me the next one 📸