A 480 N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a
ID: 1985036 • Letter: A
Question
A 480 N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 90-N rod as indicated in the figure below. The left end the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical.
horizontal component 2Your response differs from the correct answer by more than 10%. Double check your calculations. N vertical component 3
Your response differs from the correct answer by more than 10%. Double check your calculations. N
Explanation / Answer
(a)
balancing moment of weight of sign, weight of rod and tension, T, in the cable,
(500) * (4) + (90) * (3) = T * (6cos30°)
=> T = (2270) / (6cos30°) = 436.86 N
(b)
Balancing forces in the horizontal direction,
horizontal component of force of the rod by the hinge,
F(h) = Tsin30° = 436 * (1/2) = 218 N towards right
Balancing all forces in the vertical direction,
vertical component of force of the rod by the hinge,
F(v) = 500 + 900 - Tcos30° = 1400 - 436.86cos30 = 1021.67 N upwards
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