A 25.0-kg floodlight in a park is supported at the end of a horizontal beam of n

Question

A 25.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole as shown in the figure below. A cable at an angle of = 31.0° with the beam helps support the light.

a) By computing torques about an axis at the hinge at the left-hand end of the beam, find the tension in the cable.

b)Find the horizontal component of the force exerted by the pole on the beam. (magnitude and direction)

c) Find the vertical component of this force. (magnitude and direction)

Now solve the same problem from the force diagram from part (a) by computing torques around the junction between the cable and the beam at the right-hand end of the beam.

d) Find the vertical component of the force exerted by the pole on the beam.  (magnitude and direction)

e)Find the tension in the cable.

f)  Find the horizontal component of the force exerted by the pole on the beam. (magnitude and direction)

Explanation / Answer

Writing the torque equation about the hinge.

250*L - TLsin (31) = 0

T = 485 N

b) F = T cos(31) = 415 N

c) Fv= 250 - Tsin(31) = 0

d)

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