Beam Floodlight

Physics homework help on static equilibrium?

A floodlight with a mass of 15.0 kg is used to
illuminate the parking lot in front of a library.
The floodlight is supported at the end of a
horizontal beam that is hinged to a vertical
pole, as shown. A cable thatmakes an angle of
12.0◦ with the beam is attached to the pole to
help support the floodlight. Assume the mass
of the beam is negligible when compared with
the mass of the floodlight.
The acceleration of gravity is 9.81 m/s^2 .

Find the force, Ftension, provided by the cable.
Answer in units of N.

weight of the floodlight= m * g = 15*9.81 N = 147.15 N
upward force given by the cable = T * sin(12) where T is the tension in the cable.
let the length of the beam be 'h' and the distance from the hinge to the point where the cable is attached be 'x'. the torque of the floodlight on the beam must be balanced by the upward torque of the cable.

so, m*g*h = T*sin(12)*x

T=147.15*h/(x*.208)=> T=707.45*h/x N

note that we do not know where the cable is attached to the beam.

Assuming that it is attached at the end point (where the light is also attached) h = x => T = 707.45 N

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Find the horizontal force exerted on the beam by the pole. Answer in units of Newtons.?

A 60.8 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A cable at an angle od 39.3 degrees with the beam helps support the light. The acceleration of gravity is 9.8 m/s/s. Find the horizontal force exerted on the beam by the pole. Answer in units of N.

Since the system is not accelerating, ΣF=ma=m(0)=0.

By summing all forces in the y direction (taking upward as the +y direction and to the right as +x) we have

ΣFy= -mg+Tsin39.3=0 (T is the tension in the cable.) Solving this equation for T, we find that T=940N.

We now need to sum the forces in the x direction.

ΣFx= Tcos39.3 - Fpb=0 ( Fpb is the force of the pole on the beam). By plugging in T=940N, we find that Fpb=727.41N.

In order to solve this problem, you need to realize that the only forces acting in the horizontal are the x-component of the tension in the cable and the force of the pole on the beam. Since this is an equilibrium problem, they must be equal.