Question

A 35.0 kg uniform beam is attached to a wall with a hinge while its far end is supported by a cable such that the beam is horizontal. If the angle between the beam and the cable is θ = 59.0° what is the tension in the cable?

Answer 1

The tension in the cable supporting the uniform beam is 169.7 N.

Step-by-step explanation:

To find the tension in the cable supporting the uniform beam, we can analyze the forces acting on the beam. In this case, we have the weight of the beam acting downwards and the tension in the cable pulling upwards at an angle of 59.0° with the beam.

Using the principles of static equilibrium, we can set up equations for the vertical and horizontal forces. The vertical components of the tension and weight should balance each other, and the horizontal components should cancel out. From these equations, we can calculate the tension in the cable.

Tension = Weight of beam * cos(θ) / sin(θ)

Substituting the given values, we get:

Tension = 35.0 kg * 9.8 m/s^2 * cos(59.0°) / sin(59.0°)

Tension = 169.7 N

Answer 2

200.077 N

Step-by-step explanation:

Mass of beam m= 35.0kg

This is a torque problem

Sum of torques should be zero for equilibrium

Marque along point A is

weight force × half legth of beam - T sin (59°) × Length of the beam=0

35.0 × 9.8 × L/2 = T × 0.8571673007 × L

==> 343 /2 = T× 0.8571673007

==> T= 200.077 N