Question

Determine the tension force that the horizontal cable exerts on the 20kg beam as shown. 420 N 1.0 m1 0.7 m 15"

Answer 1

The tension force in a horizontal cable supporting a static object is calculated by considering the object's weight, gravitational acceleration, and any other forces or accelerations involved, based on the principles of static equilibrium.

Step-by-step explanation:

I'm afraid I don't have a visual representation of the setup you mentioned, but I'll try to assist you based on the information provided.

To determine the tension force in the horizontal cable, we can use the equation for rotational equilibrium. The torque
`(\(\tau\))` acting on the beam must be zero for rotational equilibrium. The torque is given by the product of the force and the lever arm.

`\[ \tau = r \cdot F \]`

In this case, the tension force (\(F\)) in the horizontal cable is creating a torque. Assuming there are no other torques involved, the torque equation becomes:

`\[ \tau = r \cdot T \]`

where:

-r is the lever arm (perpendicular distance from the point where the force is applied to the axis of rotation),

- T is the tension force.

Since the system is in rotational equilibrium, the sum of the torques must be zero:

`\[ \tau_{\text{clockwise}} + \tau_{\text{counterclockwise}} = 0 \]`

If the tension force is the only force causing torque, and it acts at a perpendicular distance of r from the axis of rotation, the equation becomes:

`\[ r \cdot T = 0 \]`

Now, you mentioned a 20 kg beam. If the beam is in equilibrium, it means there is no net torque acting on it. The perpendicular distance from the axis of rotation to the point where the tension force is applied is given as r .

`\[ r \cdot T = 0 \]`

If r is not zero, then the tension force T must be zero for the beam to be in equilibrium.

If r is zero, then there is no lever arm for the tension force, and it can be any value.