ENG1011 Chap.2 Free-Body Diagrams and Particle Equilibrium
Free-Body Diagrams and Particle Equilibrium
Free-Body Diagrams and Particle Equilibrium covers the second half of Week 1 and the single most assessed skill in the unit. A free-body diagram isolates one body and shows every external force acting on it, including the reactions that replace removed supports, with a coordinate system and the dimensions later equations will need.
When all forces pass through one point, the body behaves as a particle: it cannot rotate, so equilibrium reduces to the x components summing to zero and the y components summing to zero. Two equations solve two unknowns, which is why particle problems involve a ring or knot held by two cables or a cable and a strut.
The Week 6 Content Test includes a free-body diagram drawn by hand worth 10 of its 30 marks, and the practice test solutions publish how those marks split between geometry and axes, support reactions, and applied loads. Drawing unknown cable forces as tension and reading a negative result as a reversed direction builds the sign habit that trusses and frames use later.
The free-body diagram returns in every later week.
Beams, trusses, frames and machines are all solved by isolating something and drawing every force on it, so the time spent here pays back across the whole semester. The practice test's diagram task shows a whole structure with several support types, a distributed load, an applied moment and inclined forces, and asks you not to replace the distributed load or calculate the reactions.
That task rewards completeness and labelling rather than arithmetic, so the checklist of reactions, loads, dimensions and axes is worth rehearsing until it is automatic.
What this chapter covers
- 01
What a free-body diagram must show and what it must leave out
- 02
Replacing each support by the reactions it supplies
- 03
Particles: forces through one point and no rotation
- 04
Two equilibrium equations for two unknown forces
- 05
Converting mass to weight with the acceleration due to gravity
- 06
Drawing unknowns as tension and reading negative answers
- 07
How the Content Test marks a hand-drawn diagram
Worked example · free
Tensions in two cables holding a 1000 N load
- 1Draw the ring with the 1000 N weight downward and both cable forces pulling away along the cables.
- 1Horizontal balance: T1 cos 30 = T2 cos 60, so T2 = 1.732 T1.
- 1Vertical balance: T1 sin 30 + T2 sin 60 = 1000, which becomes 0.5 T1 + 1.5 T1 = 1000, so T1 = 500 N.
- 1Back-substitute: T2 = 1.732 times 500 = 866 N. Both are positive, so both cables are in tension.
Key terms
- Free-body diagram
- A drawing of one isolated body with every external force and moment that acts on it.
- Particle
- A body treated as a point because every force on it passes through one point, so it cannot rotate.
- Tension
- An axial force that stretches a cable or member, drawn pulling away from the joint it acts on.
- Compression
- An axial force that shortens a member, shown by a negative result when tension is assumed positive.
Free-Body Diagrams and Particle Equilibrium FAQ
What earns the marks on a free-body diagram?
The practice test solutions split the 10 marks into 2 for geometry, dimensions and a coordinate system, 5 for every support reaction, and 3 for all applied forces and loads with correct magnitudes and placement, with deductions for each error.
Can I choose the direction of an unknown reaction?
Yes. Reactions may be drawn in any assumed direction unless the question fixes one. The equilibrium equations then return a negative value if the assumption was wrong, and you report that the force acts the other way.
What value of g should I use?
The unit's worked solutions use 9.8 metres per second squared. Use whatever value a paper states, write the converted weight on your diagram, and keep it consistent across every part of the question.
Why do flatter cables carry more tension?
Only the vertical component of a cable's tension holds a load up. As a cable flattens, the sine of its angle shrinks, so the tension must grow to supply the same vertical component. Two cables at 25 degrees below the horizontal each carry more than the hanging weight.
Exam move
Draw a free-body diagram for every statics question you practise, even when the question does not ask for one, and mark it yourself against the published split of geometry, reactions and loads. Time yourself on particle problems: a two-cable ring should take under five minutes from diagram to checked answer. Finish each one with a quick check of the horizontal balance using the tensions you found.
Keep a one-page list of support symbols and the reactions each supplies, and use it to self-mark every diagram you draw.
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