Analysis: Revealing forces

Who has seen the wind? Neither I nor you, but when the leaves hang trembling, the wind is passing through. Christina Rossetti. In the real world, you can’t see a force. You know if one is there because of what it does like stretch a rubber band. But you are about to encounter a virtual world where forces are revealed– the world of the free-body diagram, a step towards gaining engineers’ eyes. And you will need to be able to reveal forces when you design your loudspeaker support cables. Here’s a loaded transducer. Something stretched it, so forces must be acting. We’ll show you how an FBD can reveal them. Now, the next three steps are vital. Follow carefully. Step 1.

Choose a body to analyse. I’ve chosen the entire force transducer and its load. Step 2. Represent the body separated from its surroundings, a free-body. We have used a photo of the body in mysterious darkness. Step 3. Add force arrows where the body interacted with its surroundings. We’ll back up and consider these two forces separately. We’ll show the weight first. Sir Isaac Newton said the earth mysteriously pulls down on all objects. That’s gravity. The pull on an object is its weight. It’s a force.

We’ll show it on the diagram as a bold arrow. I like red. Its tail or head should be at the centre of gravity. Centre of gravity will be explained later. Now, for the top of the assembly, we must replace the missing interaction by a force arrow. This is a magic moment. It’s a complete free-body diagram or FBD. Well, actually this is more of a free-body picture. A schematic is more usual, like this. The zigzag line shows that the transducer is elastic like a spring. But why draw the new force vertically up? Well, the way it acts downwards. The force on the transducer must balance it.

So, one, it must act vertically upwards and, two, its magnitude must be w, assuming that I can neglect the weight of the transducer. Also, when there are just two forces, they must lie along the same line of action too, as we’ll explain in a later video. It’s the principle of equilibrium. Newton’s First Law of Motion. If a body is stationary, then there is no net force acting upon it. Any forces must cancel. To complete the story, we’ll separate the load from the transducer. Sir Isaac worked out that where you disconnect objects from each other, you must draw forces that are equal and opposite. Newton’s Third Law of Motion, to every action there is an equal and opposite reaction.

These latest forces are vertical, because the one on the weight pan must balance the weight, as before, and the one on the transducer is equal and opposite to it. With this FBD, you can now see the forces that stretch the transducer. Because they are tending to extend it, the transducer is in tension. One final point. There are standard ways to represent various types of interactions on FBDs. For now, you’ll only need to know about gravity and forces in the cables. Gravity acts downwards and at the centre of gravity. Week four deals with this. Here you can assume that you will know where the centre of gravity is.

The forces in cables and strings are assumed to act in the line of the cable at the disconnection point. If its weight is negligible, a cable can be assumed straight, and the direction is obvious. In the experiments, the string is virtually straight so this is a good assumption. Four highlights of engineering mechanics. Highlight 1. Gravity, weight acting at the centre of gravity. Highlight 2. Free-body diagram. A body shown isolated from its surroundings with forces added where the surroundings once interacted. Highlight 3. Equilibrium, Sir Isaac’s First Law of Motion. Highlight 4. Action and Reaction, Sir Isaac’s Third Law of Motion. Now that you know how to reveal forces, you are ready for the next activity on how forces add.