Single-Body Systems

Dynamic analysis of individual bodies subjected to constant applied forces.

General idea of the topic

Simple systems are those with a single body and a single axis of motion: the starting point of all translational dynamics. With them the complete method is practised in its shortest version, without constraints between bodies that complicate it.

The block on a surface introduces the decision between rest and sliding from the friction threshold. The hanging block shows how weight, tension and the acceleration of a suspended load are related and when the rope pulls more or less than the weight.

What the student is expected to understand

By the end, the student should be able to decide whether a block moves by comparing the applied force with the maximum friction, compute its acceleration if it slides and obtain the tension of a rope supporting a load that rises, falls or is still.

The student should also be able to explain why the tension changes with the acceleration of the load.

Recommended learning route

1. Block on a Surface: studies a block on a horizontal surface, the normal force, friction and the comparison with the sliding threshold.
2. Hanging Block: analyses a load hanging from a rope and how weight and tension share out according to its acceleration.

Essential physical criterion

The essential criterion is to find out first whether the system moves or not. With friction the applied force is compared with the threshold; with a suspended load, the sign of the acceleration decides whether the tension is larger or smaller than the weight. Checking the result with limiting cases avoids most sign errors.

Connection with real problems

• boxes, furniture and dragged objects.
• cranes and hoists.
• lifts and suspended loads.
• cables and ropes with a load.

Final goal of the topic

The final goal is to master the dynamics method in single-body systems and to solve the friction and suspended-load cases with confidence.