A beam rests on a pin support at one end and a roller support at the other. How many unknown force components appear on its free-body diagram?
A1 — only the roller contributes an unknown since the pin is fixed
B2 — one unknown per support
C3 — the pin contributes two force components and the roller contributes one
D4 — each support contributes two force components (horizontal and vertical)
A pin prevents translation in two directions, so it introduces two unknown force components (horizontal and vertical). A roller prevents translation in one direction only (perpendicular to its surface), introducing one unknown force component. Total: 3 unknowns — exactly matching the three equilibrium equations available for 2D statics (ΣFx = 0, ΣFy = 0, ΣM = 0). Option D is the common error of treating rollers like pins.
Question 2 Multiple Choice
When drawing a free-body diagram of a book resting on a table, which forces should appear on the diagram?
AThe book's weight downward and the table's weight downward
BThe book's weight downward and the normal force from the table upward
CThe book's weight downward, the normal force upward, and the force the book pushes down on the table
DOnly the book's weight, since gravity is the only active applied force
An FBD shows only forces acting ON the isolated body — the book. Gravity pulls the book down (its weight). The table pushes the book up (normal force). Option C includes the force the book exerts on the table, which is Newton's-third-law pair — it acts on the table, not on the book, and must never appear on the book's FBD. Including it would produce a wrong equation: the two reaction forces would cancel and predict the book floats.
Question 3 True / False
A correct free-body diagram should include most forces and moments acting on the body, including those the body exerts on surrounding objects.
TTrue
FFalse
Answer: False
An FBD includes ONLY forces acting ON the isolated body. Newton's third law guarantees every force has a reaction pair, but the pair acts on the other body. Including outward forces would mean summing forces on two different bodies simultaneously, corrupting the equilibrium equations. The isolation step exists precisely to exclude these: sever the body, replace each severed connection with the force IT provides to YOUR body, and draw nothing else.
Question 4 True / False
Once a correct FBD is complete, the remaining computation in a 2D statics problem is mechanical substitution into three equilibrium equations.
TTrue
FFalse
Answer: True
The FBD defines all forces and moments and introduces all unknowns. Writing ΣFx = 0, ΣFy = 0, ΣM = 0 is then a direct substitution of the quantities on the diagram. The intellectual work — identifying what forces exist, what directions they act, which are known, which are unknown — happens entirely at the FBD stage. This is why an incorrect FBD guarantees a wrong answer even if the algebra that follows is flawless.
Question 5 Short Answer
Why is 'isolation' — mentally severing the body from its surroundings — the core operation of the free-body diagram method?
Think about your answer, then reveal below.
Model answer: Isolation forces you to account for every mechanical connection that was constraining the body. Each severed connection must be replaced by the force or moment it was providing: a roller becomes a normal force, a pin becomes two force components, a fixed wall becomes two forces and a couple moment. Without isolation, these reaction forces stay implicit — the structure 'just works' in your imagination without exposing what forces make it work. Isolation makes every load explicit, prevents omissions, and produces exactly the inputs needed for equilibrium analysis.
The number and type of unknowns introduced by each support type is fixed by its kinematic constraint (how many degrees of freedom it removes). Knowing this mapping — roller → 1 unknown, pin → 2, fixed support → 3 — is as important as drawing the arrows. Isolation operationalizes this: it turns implicit structural action into explicit force vectors that can enter equilibrium equations.