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 net force vector F. The particle is acted on by three constant forces. Let's sum them: F_1 = 2i + j - k F_2 = k - j (which can be written as 0i - j + k) F_3 = 3i + j + 5k The net force F is the sum of these forces: F = F_1 + F_2 + F_3 F = (2i + j - k) + (0i - j + k) + (3i + j + 5k) F = (2+0+3)i + (1-1+1)j + (-1+1+5)k F = 5i + 1j + 5k F = 5i + j + 5k Step 2: Calculate the displacement vector d. The particle is displaced from point r_1 = i + 2j + 3k to point r_2 = 6i + 3j + k. The displacement vector d is given by r_2 - r_1: d = (6i + 3j + k) - (i + 2j + 3k) d = (6-1)i + (3-2)j + (1-3)k d = 5i + 1j - 2k d = 5i + j - 2k Step 3: Calculate the work done W. The work done by a constant force is given by the dot product of the force vector and the displacement vector: W = F · d W = (5i + j + 5k) · (5i + j - 2k) W = (5)(5) + (1)(1) + (5)(-2) W = 25 + 1 - 10 W = 26 - 10 W = 16 The work done is 16 units (assuming standard units like Joules if force is in Newtons and displacement in meters). The final answer is 16. That's 2 down. 3 left today — send the next one.