To find the tension in the cable supporting the steel beam, you can use the principle of mechanical equilibrium. The beam and worker are in a state of static equilibrium, which means that the net force and net torque acting on the system are both zero.
To start, let's consider the forces acting on the beam. There are two main forces to consider:
1. The weight of the beam:
The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity. In this case, the mass of the steel beam is given as 1435 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So the weight of the beam is: weight_beam = 1435 kg * 9.8 m/s^2.
2. The tension in the cable:
This is the force exerted by the cable to support the beam. Let's call this tension T.
In order for the beam to be in equilibrium, the vertical forces acting on it must add up to zero. This means that the weight of the beam must be balanced by the tension in the cable. Mathematically, this can be expressed as:
T - weight_beam = 0
Now, let's consider the torque acting on the system. Torque is a measure of the effectiveness of a force in causing rotational motion. In this case, we want to find the torque exerted by the weight of the beam about the point where it is supported by the cable.
The torque can be calculated using the formula: Torque = force * distance.
The force we are interested in is the weight of the beam, and the distance is the 2.0 m between the construction worker and the end of the beam.
So the torque exerted by the weight of the beam is: Torque_weight_beam = weight_beam * 2.0 m.
To achieve equilibrium, the net torque acting on the system must be zero. This means that the torque exerted by the weight of the beam must be balanced by the torque exerted by the tension in the cable. Mathematically, this can be expressed as:
Torque_weight_beam - Torque_cable = 0
Substituting the expressions for torque and weight_beam, we get:
(weight_beam * 2.0 m) - (T * 2.0 m) = 0
Simplifying the equation, we find:
(weight_beam - T) * 2.0 m = 0
Finally, rearranging the equation, we can solve for T:
T = weight_beam
By substituting the given value for weight_beam, you can find the tension in the cable.