A 19.0-kg floodlight in a park is supported at the end of a horizontal beam of n

Question

A 19.0-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 = 25.0° with the beam helps support the light.(a) Draw a force diagram for the beam. (b) By computing torques about an axis at the hinge at the left-hand end of the beam, find the tension in the cable. N (c) Find the horizontal component of the force exerted by the pole on the beam. magnitude N direction (d) Find the vertical component of this force. magnitude N 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. (e) Find the vertical component of the force exerted by the pole on the beam. magnitude N direction (f) Find the tension in the cable. N (g) Find the horizontal component of the force exerted by the pole on the beam. magnitude N direction

Explanation / Answer

Consider the torques about an axis perpendicular to the page and through the left end of the horizontal beam

sigma T = (T * sin 25) - (19 * 9.8)d = 0

T = 440.18 N

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sigma Fx = 0

H - T cos 25 = 0

H = 440.18 * cos 25 = 398 N [ to the right ]

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sigma Fy = 0

V + T sin 25 - 186.2 N = 0

V = 0

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