Question

a frame hanging on a wall is held by two cables. the tension in each cable is 30 n, and the cables make an angle of 45° with the horizontal, as shown in the picture. what is the weight of the frame?
a 10.2 n
b 21.2 n
c 32.4 n
d 42.4 n

Explanation:

Step1: Analyze Vertical Force

Each cable has tension \( T = 30\,\text{N} \) and angle \( \theta = 45^\circ \) with horizontal. Vertical component of tension: \( F_y = T\sin\theta \).

Step2: Calculate Total Vertical Force

Two cables, so total upward force: \( F_{\text{total}} = 2 \times T\sin\theta \). Substitute \( T = 30\,\text{N} \), \( \sin45^\circ = \frac{\sqrt{2}}{2} \approx 0.707 \).
\( F_{\text{total}} = 2 \times 30 \times 0.707 \approx 42.4\,\text{N} \). This equals the weight (equilibrium).

Answer:

D. 42.4N