A) A 1510 N uniform boom is supported by a cable as shown. The boom is pivoted a

Question

A) A 1510 N uniform boom is supported by a
cable as shown. The boom is pivoted at the
bottom, and a 2380 N object hangs from its
end.
The boom has a length of 27 m and is at an
angle of 48?
above the horizontal. A support
cable is attached to the boom at a distance
of 0.68L from the foot of the boom and its
tension is perpendicular to the boom.

Find the tension in the cable holding up the
boom.
Answer in units of N.

B) Find the horizontal component of the reaction
force on the boom by the floor.
Answer in units of N.

C) Find the vertical components of the reaction
force on the boom by the floor.
Answer in units of N.

Explanation / Answer

W1 = 1510 N, W2 = 2380 N, alpha = 48 deg, L = 27 m , L1 = 0.68 L

T(0.68 L) = W2 (L cos alpha) + W1 (L/2 cos alpha)

T = (W2 cos alpha) / 0.68 + (W1 cos alpha) / 2 * 0.68

= (2380 * cos 48) / 0.68 + (1510 * cos 48) / 2 * 0.68

= 3084.89 N

-------------------------------------------------------

Fh = T sin alpha = 3084.88 * sin 48

= 2292.5 N

--------------------------------------------------------

Fv = W1 + W2 - T cos alpha = 1510+ 2380- 3084.88 * cos 48

= 1825.8 N

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