Resolution of symmetric tensions into perpendicular components

Steps:

• Each half of the elastic exerts a tension of 4.0 N on pin X, directed along YX and XZ.
• From the diagram, each segment forms a 3-4-5 right triangle with YZ, so sin θ = 3/5 = 0.6, where θ is the angle to YZ.
• Perpendicular component of each tension in direction P: 4.0 N × 0.6 = 2.4 N.
• Net force on trolley: 2 × 2.4 N = 4.8 N (parallel components along YZ cancel).

Why C is correct:

• Newton's third law requires the unbalanced perpendicular components to sum to 4.8 N, accelerating the trolley in direction P.

Why the others are wrong:

• A: Only one perpendicular component, ignoring the second tension.
• B: Incorrect sin θ (e.g., using 0.4 instead of 0.6).
• D: Adds tensions without resolving components.

Final answer: C