A particle is suspended by two cables attached to a ceiling. The weight of the particle and both cable angles are known. How many unknown forces can be found using the 2D particle equilibrium equations?
AOne — you can only solve for the resultant cable tension, not individual tensions
BTwo — ΣF_x = 0 and ΣF_y = 0 provide two independent equations for two unknowns
CThree — weight plus two tension components gives three equations
DFour — each cable tension has x and y components, giving four unknowns
In 2D, the equilibrium conditions ΣF_x = 0 and ΣF_y = 0 yield exactly two independent equations. With two unknown cable tensions (and known weight and angles), the system is determinate: two equations, two unknowns. If a third unknown force were present, the system would be statically indeterminate. The cable tension magnitudes are the unknowns, not their components separately — components are derived from magnitude times the known angles.
Question 2 Multiple Choice
A hockey puck slides across ice at constant velocity of 3 m/s in a straight line. What is the net force on the puck?
ANon-zero — a moving object requires a net force to maintain its motion
BZero — constant velocity means zero acceleration, so ΣF = 0
CEqual to the puck's weight — gravity must be balanced by the ice reaction only
DEqual to friction force — friction is the only horizontal force and it must be overcome
Newton's second law states ΣF = ma. Constant velocity means zero acceleration (a = 0), therefore ΣF = 0. The puck is in equilibrium even though it is moving. Equilibrium does not mean 'at rest' — it means 'not accelerating.' On frictionless ice, gravity and the normal force balance vertically, and there is no horizontal net force. The misconception that motion requires a continuous net force is a pre-Newtonian intuition that statics explicitly corrects.
Question 3 True / False
A particle in equilibrium is expected to be at rest; an object moving at constant velocity is not in equilibrium.
TTrue
FFalse
Answer: False
Equilibrium is defined by zero net force (ΣF = 0), which by Newton's second law means zero acceleration (a = 0). Zero acceleration is consistent with any constant velocity, including zero velocity (rest). A car cruising at a steady 60 mph on a level highway is in translational equilibrium — engine force balances drag and friction, net force is zero, acceleration is zero. Rest is a special case of equilibrium, not its definition.
Question 4 True / False
If a particle system has three unknown force magnitudes in 3D, the three equilibrium equations (ΣF_x = 0, ΣF_y = 0, ΣF_z = 0) are sufficient to solve for all three unknowns.
TTrue
FFalse
Answer: True
In 3D, particle equilibrium provides three independent scalar equations — one per coordinate direction. With exactly three unknowns, the linear system is determinate and can be solved algebraically. If there were four or more unknowns, the system would be statically indeterminate, requiring additional information (material stiffness, deformation compatibility) beyond what statics provides. The match between number of unknowns and available equations is what determines solvability.
Question 5 Short Answer
Why is drawing a complete free-body diagram considered the actual solution method in particle equilibrium, rather than just a preliminary sketching step?
Think about your answer, then reveal below.
Model answer: The free-body diagram is the mathematical model, not an illustration of it. Every force included in the FBD appears as a term in the equilibrium equations; every force omitted is a term missing from those equations. If a cable, normal force, or component of weight is left out of the FBD, the equilibrium equations are wrong — they represent a different physical situation. Getting the FBD right is equivalent to writing down the correct equations. The algebra that follows is mechanical; the engineering judgment lives entirely in the FBD.
This is why instructors insist on drawing FBDs before writing any equations. It's not formalism — it's the step where assumptions are made explicit: which forces act, in which directions, on which body. A systematic FBD forces you to account for all interactions and prevents the most common errors (missing the weight, forgetting that each cable exerts a separate tension). The equations are just the FBD translated into algebra.