Question

A vendor hangs an 8.0 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in the figure. What is the tension in the cable?

A vendor hangs an 8.0 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in Figure P8.8. What is the tension in the cable?

Answer 1

Concepts and reason

The concept required to solve the given question is the equilibrium of forces acting on the sign board. That is, the parallel and perpendicular forces acting on the object and the tension in the cable.

First, find the different types of forces that are acting on the sign board. Then resolve the force in the component form. Then, find the component of force which is equal to the tension acting in the cable.

Fundamentals

Tension acting in the cable:

Force acting on a body may be defined as the sudden push or pull which is capable of changing the direction of motion of the object when it is unopposed. It is a vector quantity which has both magnitude and direction.

Force can be resolved into its component form as x and y components of forces. The parallel component is x – component and the perpendicular component is y – component.

Normal force acting on the object is equal and opposite to the gravitational force applied on the object.

$N=mg $

Here, N is the normal force acting on the object, m is the mass, and g is the acceleration due to gravity.

Tension force is defined as the “force that is transmitted through a string, rope cable or wire when it is pulled tight by forces acting from opposite ends”. It is directed along the length of the wire that pulls the objects equally on the opposite ends of the wire.

Normal force acting on the object,

$N=mg $

Substitute 8 kg for m and for g.

Resolve the tension force into its components acting in the cable.

Expression for horizontal component of tension is,

Here, is the horizontal component of tension.

Vertical component of tension,

Here, is the vertical component of tension.

Vertical component of force acting on the sign board,

Rearrange the above expression for the tension acting on the cable,

Substitute 78.4 N for N and for in the above expression.

Ans:

Tension acting in the cable is .