A photo frame weighing 4.16 newtons is hanging by a wire making an angle with the horizontal. The tension experienced by both wi
res is 3 newtons. What angle is made by both wires with the horizontal?
A. 13.7º
B. 24.3º
C. 43.9º
D. 45.4º
E. 49.2º
A. 13.7º
B. 24.3º
C. 43.9º
D. 45.4º
E. 49.2º
2 answers:
Answer: option C. 43.9°
Explanation:
Refer to the diagram. The tension in the two strings is equal T₁=T₂=T = 3 N
The strings support a frame weighing, W= 4.26 N
We will write the tension in the strings as the sum of their horizontal and vertical components.
The horizontal components balance each other and cancel out.
T₁ cos θ = T₂ cos θ
On the other hand, The vertical component would support the weight of the frame.
2 T sin θ = W
2 × 3 N × sin θ = 4.16 N
sin θ = 0.693
⇒ θ = sin ⁻¹(0.693) = 43.9°
Hence, the angle made by two wires with the horizontal is 43.9°.
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