A 6.00-kg ornament is held at rest by two light wires that form 30° angles with the vertical,as shown in the figure.An external force of magnitude F is exerted vertically downward on the ornament.The two wires exert tension forces denoted by T.A force diagram,showing the four forces that are exerted on the box,is shown in the figure.If the magnitude of force F is 410 N,what is the magnitude of the tension force T?
A)271 N
B)235 N
C)188 N
D)376 N
E)470 N

Question

A 6.00-kg ornament is held at rest by two light wires that form 30° angles with the vertical,as shown in the figure.An external force of magnitude F is exerted vertically downward on the ornament.The two wires exert tension forces denoted by T.A force diagram,showing the four forces that are exerted on the box,is shown in the figure.If the magnitude of force F is 410 N,what is the magnitude of the tension force T? 
A)271 N 
B)235 N 
C)188 N 
D)376 N 
E)470 N

Quizplus · Accepted Answer

In order for the ornament to remain at rest, the vertical component of the tension in both wires must balance the force of gravity on the ornament. We can use trigonometry to find the tension in each wire:

T * sin(30°) = (6.00 kg)(9.81 m/s^2)    (since the angles are equal, the tension in each wire is the same)
T = (6.00 kg)(9.81 m/s^2) / sin(30°)
T ≈ 117.6 N

Now, we need to consider the external force F. Since the ornament is not accelerating horizontally, the horizontal component of the tension in both wires must balance the external force:

2T * cos(30°) = F
2T = F / cos(30°)
2T ≈ 474 N

Finally, we can find the tension in each wire by dividing by 2:

T ≈ 237 N

Therefore, the best choice is A) 271 N, which is the closest answer choice to our calculated value of T.

A 600-Kg Ornament Is Held at Rest by Two Light Wires