Question

Explain the need for tall towers on a suspension bridge to ensure stable equilibrium.

Short answer

Tall towers increase the upward force that balances the bridge.

Step-by-step solution

Equilibrium

Equilibrium is described as a condition of rest in which nothing changes. There will be no positive or negative energy transfers in a balanced body.

Diagram

For the equilibrium of any object, the sum of total torques and the sum of total forces on the object should be zero.

We consider the diagram for a bridge as shown below:

The tension along the suspension cable acts towards the length of the cable. The horizontal component of the tension is,

$T\cos \theta$

The vertical components are,

$T\sin \theta$

Explanation

The horizontal components cancel each other, but the sum of the vertical parts balances the bridge's downward weight.

The shorter towers give a slight slope and a small angle value, giving a slight upward force. For these cases, the compressive forces on the towers will be greater than the upward force. So, the towers can compress, and their equilibrium will be disturbed.

Thus, the tall towers increase the upward force that balances the bridge providing greater upward forces.