A 23.0-kg floodlight in a park is supported at the end of a horizontal beam of n

Question

A 23.0-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 = 34.0°with the beam helps support the light.

(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

N

(d) Find the vertical component of this force.

N

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.

N

(f) Find the tension in the cable.
N

N

Explanation / Answer

here,

mass of light , m = 23 kg

theta = 34 degree

(b)

let the tension in the cable be t

equating the torque about the hinge

t * sin(theta) * l - m * g * l = 0

t * sin(34) - 23 * 9.8 = 0

t = 403.08 N

the tension in the cable is 403.08 N

(c)

let the horizontal component of the force exerted by the pole on the beam be Fx

Fx - t * cos(theta) = 0

Fx = 403.08 * cos(34)

Fx = 334.17 N

(d)

the vertical component of this force be Fy

Fy - m*g + t * sin(theta) = 0

Fy - 23 * 9.8 + 403.08 * sin(34) = 0

Fy = 0

(e)

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