Question

A framed picture hangs from two cords attached to the ceiling.

A picture of a picture frame hanging by two cables at the center of the frame at the same length and angle from the vertical.

Which shows the correct free body diagram of the hanging picture?

A free body diagram with two force vectors, the first pointing downward labeled F Subscript g Baseline, the second pointing upward labeled F Subscript N Baseline.

A free body diagram with three force vectors, the first pointing south labeled F Subscript p Baseline, the second pointing northeast labeled F Subscript T Baseline, and the third pointing northwest labeled F Subscript N.

A free body diagram with three force vectors, the first pointing south labeled F Subscript g Baseline, the second pointing northeast labeled F Subscript T Baseline and the third pointing northwest labeled F Subscript T.

A free body diagram with two force vectors, the first pointing downward labeled F Subscript p Baseline, the second pointing upward labeled F Subscript T Baseline.

Answer 1

The third diagram is correct: one downward force (weight, F_g) and two tension forces (F_T) along the two cables, pointing up-left and up-right.

Reason: the picture is in static equilibrium so the two cable tensions (symmetric) provide the upward components that balance the weight: 2T cosθ = W (θ is the angle from the vertical). The other diagrams are wrong because there is no single normal/vertical support and there are indeed two tension forces, not just one.