Free-Body Diagrams

System boundaries and force inventory

A free-body diagram isolates one selected object or system. Every arrow represents an external interaction acting on that selected boundary. Motion arrows, coordinate axes, and forces exerted by the selected object on its surroundings are excluded. Fix the system boundary before judging the diagram complete. The same rope force is external to a block but internal to a block-rope system.

Field interactions belong in the inventory even when no object touches the selected body. Gravity, electric fields, and magnetic fields have sources outside the drawn boundary and contribute force arrows only when the stated model predicts a coupling. Labeling the source prevents a field force from being confused with a contact reaction or with a coordinate-direction arrow.

The resulting component equations are

\sum F_{x} = m a_{x}, \sum F_{y} = m a_{y},

with axes selected to match the geometry. A negative solved force means the assumed arrow direction is opposite the physical direction; it does not invalidate the equation.

A block isolated from its surroundings. Only external interactions are drawn: the upward normal force N, the downward weight mg, and a horizontal applied pull.

Contact and incline constraints.

The normal force is perpendicular to the local contact surface. Its magnitude is not universally $m g$ ; it follows from the normal component equation. For a block on an incline at angle $θ$ with no acceleration normal to the surface,

N - m g cos θ = 0, N = m g cos θ .

Along the incline, gravity contributes $m g sin θ$ downhill. Static or kinetic friction, when present, is tangent to the surface. These axes avoid resolving the normal force itself and place the constraint directly in the normal equation.

Incline-aligned axes for a block on a slope. The normal force N is perpendicular to the surface, friction f acts along it, and the weight mg is vertical.

Strings, pulleys, and connected bodies.

An ideal massless taut string has one tension magnitude along a straight segment. A frictionless massless pulley changes tension direction but not magnitude. String length constrains the accelerations of connected objects. For a simple two-mass pulley system, the accelerations have equal magnitudes and opposite directions.

A massless string transmits one tension around an ideal pulley, so the two hanging masses share a single tension magnitude and equal, opposite accelerations.

For $m_{1}$ descending and $m_{2}$ rising,

m_{1} g - T = m_{1} a, T - m_{2} g = m_{2} a .

Addition removes tension and produces

a = \frac{( m _{1} - m _{2} ) g}{m _{1} + m _{2}} .

This holds in the ideal model: massless string, frictionless massless pulley, and a taut string throughout, so the two blocks share one acceleration magnitude and one tension.

Diagram construction and coordinate choices

Write an interaction inventory before drawing a free-body diagram. State the selected body, list every object that touches it or acts on it at a distance, and translate each interaction into one force arrow on the selected body. A table can exert a normal force and perhaps friction; Earth exerts weight; a string exerts tension along its own direction; a hand, spring, or motor can exert an applied contact force. Each item should have an identifiable source.

The inventory prevents double counting of contact and gravitational interactions. “Normal force” and “support force” are usually two names for the same contact interaction, not separate arrows. A block does not receive both $m g$ and a second “gravity force.” The reaction force to the block's weight acts on Earth and belongs on Earth's diagram, not on the block's. Likewise, an acceleration arrow may be placed nearby as analysis information, but it is not one of the forces in the sum.

The number of arrows is set by interactions, not by the number of coordinate axes. A two-dimensional diagram can have three, four, or more external forces. Conversely, a body moving in a curved path can have only one external force. Coordinates are chosen after the interactions are identified, so an inconvenient axis never causes a real force to disappear from the inventory.

Applied-force labels need a physical source as well. “Pull” may denote a hand, a motorized cable, a spring, or a fluid actuator; those models can impose different directions, time dependences, and reaction forces. State the source whenever later parts of the calculation require a system boundary or a third-law partner.

A lamp hangs motionless from a vertical cable. The selected body is the lamp. Its inventory contains cable tension upward and Earth's gravitational force downward. The ceiling exerts a force on the cable, not directly on the lamp. Adding a ceiling force to the lamp diagram would introduce a nonexistent interaction and produce an incorrect three-force balance.

Choose axes to match the constraint geometry. A block on a straight incline is often simplest with one axis tangent to the surface and one normal to it. The contact constraint then gives a direct normal-acceleration condition, usually $a_{⊥} = 0$ . A horizontal-vertical basis remains valid, but it forces the normal force and any friction force to be resolved into components, producing more algebra without adding information.

The direction of a constraint force follows the geometry. A smooth surface can push perpendicular to itself but cannot pull an unattached object toward itself. A taut string pulls along its length and has no compressive response. A negative solved tension under the selected sign convention means the string has gone slack, so the fixed-length constraint no longer applies. A rigid rod may push or pull, which is why a rod model and a string model cannot be exchanged casually.

Normal force is determined by the normal component equation. It equals $m g$ only when the surface is horizontal and normal acceleration is zero with no other normal forces. An elevator floor, a curved track, an inclined plane, or a hand pressing on the body changes the result. The normal arrow should therefore be drawn first from the contact geometry and assigned a magnitude only after the component equation is written.

Tension models and string-length constraints.

The statement “the tension is the same everywhere” belongs to an ideal model with a massless taut string and frictionless massless pulleys. It is not a universal property of rope. A massive rope can have different tension at different locations because each segment must accelerate its own mass. A pulley with rotational inertia or axle friction can support unequal tensions on its two sides. A slack string has zero tension and imposes no length constraint until it becomes taut again.

An ideal straight string connecting two bodies has fixed length that links their displacements. Select one positive coordinate for each body and express total string length in those coordinates. Differentiating once gives the velocity relation and twice gives the acceleration relation. Signs follow the coordinate definitions. The familiar “equal magnitudes, opposite directions” result is only one special choice of coordinates for a simple one-pulley arrangement.

A movable pulley introduces a factor of two. If the moving pulley is supported by two segments of the same string, raising the pulley by a distance $y$ shortens both segments by $y$ . The free end must provide $2 y$ of string. Its speed and acceleration therefore have twice the magnitude of the pulley's values, with direction set by the chosen coordinates. Draw the full string path before differentiating the length constraint; the two supporting segments set the factor of two.

A movable pulley is held by two string segments. One end is fixed to the ceiling; the string passes under the movable pulley that carries the load, up over a fixed pulley, and down to the free end. A unit rise of the load shortens each supporting segment, so the free end must be pulled down through twice that length.

Let downward displacement of the free end be $x$ and upward displacement of the movable pulley be $y$ . Apart from fixed portions, string length is $x - 2 y$ . Since the string is taut, $x - 2 y$ is constant. Thus $v_{x} = 2 v_{y}$ and $a_{x} = 2 a_{y}$ . If the free end is pulled down at $0.80 m s^{- 1}$ , the pulley and attached load rise at $0.40 m s^{- 1}$ . The factor is geometric; it does not depend on the mass of the load.

Connected systems and force models

Connected-body problems usually need more than one diagram. An individual-body diagram retains tension and contact forces because they act externally on that one body. A combined-system diagram removes forces between bodies inside the selected boundary. The combined-system equation can be short because internal forces cancel. An internal tension or contact force still requires an individual-body diagram after the common acceleration has been found.

The system boundary should be selected to match the question. For two blocks joined by a string on a smooth table, choosing both blocks as the system removes tension from the horizontal external-force sum. Choosing one block retains tension and is necessary to find it. Neither diagram is more correct; each answers a different part of the problem. Mixing an internal tension cancellation from the two-block system with a one-block mass on the right side is an inconsistent boundary change.

One connected pair, two boundaries. Tension is external on either isolated block but internal to the two-block system, where it cancels from the momentum balance.

Contact models beyond a level surface.

Contact constraints are local. The normal direction is perpendicular to the surface at the point of contact, even when the surface is curved. A bead inside a circular track has a normal force directed toward the centre if it remains pressed against the inside surface; a bead on the outside receives a normal force away from the surface. The force direction follows the side of contact, whereas the required normal acceleration follows the trajectory geometry. These are separate facts and should not be inferred from a memorized sign alone.

A surface can lose contact. The normal force cannot become negative for a simple unattached contact, because the surface cannot pull the body toward itself. A solved value $N < 0$ means the assumed contact has already failed; the replacement model has $N = 0$ and a new unconstrained trajectory. This interpretation is essential for objects cresting a hill, a block on a track, or a vehicle crossing a curved bridge.

Friction belongs in the tangential direction and depends on the contact model. Static friction is an adjustable response up to its limiting magnitude; it is not automatically equal to $μ_{s} N$ . Kinetic friction is used only while sliding and points opposite the relative sliding direction. If the direction of impending motion is uncertain, choose a trial friction direction, solve the equations, and interpret a negative answer as reversal of the assumed direction.

A local normal-tangent basis at a point on a curved guide. The normal force follows the surface and can vanish where contact is lost; the weight stays vertical.

A connected system requires a separate free-body diagram for every body whose force balance is needed. Mark a positive coordinate for each diagram and write the constraint relation in the same coordinate language. Only then write component equations. This order prevents signs from being carried informally from one diagram to another, especially when one body moves vertically while another moves along an incline or a table.

Unknowns usually include acceleration, tension, normal force, and perhaps friction. The count of independent equations must match the unknowns after the constraint relations are included. A string-length relation imposes an equation even though it is not a force equation. Conversely, writing Newton's second law for a combined system and for all members can create redundant equations; select independent equations that determine the requested quantities without subtracting the same information twice.

After solving, test each force against its model. Tension must be nonnegative for a taut string, normal force must be nonnegative for simple contact, and static friction must not exceed its maximum magnitude. A violation does not signal failed algebra. It signals that the assumed constraint state—taut string, contact, or sticking—was physically inconsistent and must be replaced by a different case.

A coupled pair gets one free-body diagram each plus a shared constraint. The string transmits equal tensions; the linking equation ties the two accelerations.

Audit a completed free-body diagram before calculation. Every arrow must name an interaction source rather than a direction such as “up.” Every force must act on the selected body rather than on a neighboring object. Contact forces should match the local surface direction, and string forces should follow the string. An unattached surface supplies no normal force, and a slack rope supplies no tension. Apply these checks instead of relying on a standard arrow pattern.

State the chosen axes. Resolve only forces that are not already aligned with an equation axis. A component equation must include every force component along that axis, including components that oppose the assumed positive direction. The acceleration component belongs on the right side and is determined by the motion constraint; it is not selected to make the algebra convenient.

Compare the solved signs and magnitudes with the model. A negative normal or tension identifies a changed contact or string state. A static-friction value larger than its limit identifies impending slip. These outcomes are part of the physical solution: they state that the original free-body diagram described a trial case, not the realized constraint configuration.

Clear arrows make later algebra auditable. Ambiguous arrows create ambiguous components, while an isolated body exposes the model assumptions before numerical substitution.

Distributed loads and string constraints

Some contacts act over an extended region rather than at a single geometric point. A floor supports a box through a distributed pressure over its base; a beam support may apply forces across a bracket; a fluid exerts pressure over a surface. A free- body diagram at introductory scale often replaces this distribution by one resultant force. The resultant has the same total force and the same net turning effect about the points relevant to the model. Its line of action is therefore part of the replacement, not a decorative placement of an arrow.

Uniform load density on a symmetric contact region places the resultant through its geometric centre. A nonuniform load shifts it toward the more heavily loaded side. A block resting level on a broad table can be modelled by one normal resultant through the base centre when no tipping tendency is present. If an applied force shifts the load distribution toward an edge, the resultant shifts with it. Once its line of action reaches the edge, the contact model may change to impending tip; beyond the edge, the original full-base contact is impossible.

The distributed contact is still one interaction category, but its resultant can have more modelling content than a point-contact normal force. A diagram should state whether the arrow represents an ideal point contact or an equivalent resultant of a spread load. This distinction matters whenever torque, stability, or partial loss of contact is being analysed.

A crate base is $0.80 m$ wide. A horizontal push at the top shifts the normal resultant $0.25 m$ from the base centre toward the leading edge. The edge lies $0.40 m$ from the centre, so the crate remains in full contact under the point-resultant model. A calculated shift of $0.46 m$ would not mean a larger normal force; it would mean that the full-base contact assumption has failed and a tipping or new-contact model is required.

Multi-segment strings are handled by writing total variable length explicitly. Each straight segment contributes its signed coordinate length. Portions wrapped around fixed pulleys and distances between fixed supports are constants and disappear on differentiation. The resulting length equation is often simpler than the drawing first suggests, but only after every variable segment has been counted once.

A load supported by $n$ vertical segments of the same ideal string shortens all $n$ segments during upward displacement. The free end must therefore move $n$ times as far in the opposite sense. Differentiating gives the corresponding velocity and acceleration factors. This relation is purely kinematic. The force advantage comes from the same geometry through the multiple tension segments, but the two arguments should not be merged into one unexplained rule.

Coordinate signs matter. If both the free-end coordinate and the load coordinate are defined downward, a typical relation is $x + n y = constant$ , giving $a_{x} = - n a_{y}$ . If one coordinate is upward and the other downward, the same physical constraint may appear with the opposite sign. State the coordinates beside the diagram before differentiating so that a later negative acceleration has a clear meaning.

With downward free-end coordinate $x$ and upward load coordinate $y$ , the variable string length is $x - 3 y$ . Tautness gives $x - 3 y = constant$ and therefore $a_{x} = 3 a_{y}$ . Pulling the free end downward with acceleration $1.2 m s^{- 2}$ raises the load with acceleration $0.40 m s^{- 2}$ . The relation would be invalid if one segment went slack, because the string length would no longer constrain all parts of the system.

Inclined contact with applied forces.

Inclines become more subtle when an applied force is not parallel to the surface. The normal force then depends on both gravity and the applied force's normal component. A pull angled away from the surface can reduce contact pressure; a push into the surface can increase it. The free-body diagram should show the actual pull direction before it is resolved. Replacing it prematurely with an along-slope arrow erases the component responsible for changing the normal force and, consequently, any friction limit.

A block on a fixed incline uses an incline-aligned basis that separates tangent and normal components. The no-penetration constraint determines the normal acceleration condition while contact persists. The tangential equation determines whether the block speeds uphill, slows while moving uphill, remains at rest, or slides downhill. Static friction has whatever tangent direction is needed to oppose the anticipated relative motion, subject to its magnitude limit. It should not be assigned from the current direction of a block that may still be at rest.

A single incline geometry permits two trial friction directions. One trial places friction uphill because gravity tends to draw the block down. Another places friction downhill because a strong applied pull tends to drag the block up. The solved sign selects the physically consistent direction. This procedure is cleaner than memorizing a fixed friction arrow for every incline.

A pull applied at an angle to an incline has both an along-surface component and a normal component; the latter changes N and the available friction.

Curved paths and frame selection

On a curved guide, the normal and tangent directions rotate from point to point. The diagram should be drawn at the specific location under analysis, not with a single global “up” and “right” copied around the curve. The normal direction points toward the local centre of curvature for the usual inward-positive choice, while the tangent direction follows the instantaneous path. Weight, contact force, and any friction must be projected onto these local directions.

The normal component of acceleration is set by speed and curvature, whereas the tangent component is set by change in speed. This separation is a kinematic constraint attached to the path. A body may have zero tangential acceleration while still requiring a nonzero normal force, or it may change speed on a straight guide with no curvature at all. Conflating the two creates the false rule that every normal force equals weight or that every force along a curve changes speed.

Contact side again matters. An object inside a loop receives an inward normal from the track; an object on the outside receives an outward normal. Before writing a component equation, mark the contact side and draw the force in the direction the surface can actually push. The solved magnitude then tests whether that contact can be maintained.

At the side of a vertical circular track, the inward normal is horizontal while weight is vertical. Weight therefore has no normal component at that instant, even though it may have a full tangent component. A diagram that draws both normal force and weight horizontally at the side has imported the geometry from the top or bottom of the circle and cannot produce a consistent component equation.

The diagram and the coordinate frame must be declared together. In an inertial ground frame, draw only interactions exerted on the selected body and write the acceleration measured in that frame. A frame moving at constant velocity changes coordinate values but does not require a new force inventory. An accelerating frame can be convenient for describing relative positions, but its diagram requires a clearly labelled inertial term if that frame is used for force equations. Mixing a ground-frame acceleration with forces interpreted in a vehicle frame is not a change of notation; it is an inconsistent model.

Use one inertial frame for the free-body diagrams and express constraints relative to the guides or supports in that same frame. For example, a block held against an accelerating wall has a normal force due to the wall contact, while its no-separation condition states that the block shares the wall's normal acceleration. The wall acceleration is not a force arrow. It appears in the kinematic constraint that connects the diagram to the motion.

Equation consistency can be checked before solving. Each isolated body has one component equation per selected axis. Each string or rigid linkage imposes a geometric relation. Each contact state imposes a condition such as zero normal relative acceleration, nonnegative normal force, or a friction bound. List unknowns beside these relations. If a tension, normal force, and common acceleration are unknown, the set must contain enough independent statements to determine them, but duplicating a system equation that is merely the sum of two individual equations does not add information.

After a solution, substitute the values back into every diagram separately. Internal forces must appear with equal magnitude and opposite direction on the two bodies they connect. Apply constraint checks after the algebra: a computed negative tension, negative normal, or excessive static-friction magnitude identifies the diagram that requires revision. The check ties each solved value to its physical constraint state.

If a block is pressed against a vertical guide that accelerates horizontally, the normal direction is horizontal and the no-separation condition concerns horizontal acceleration. Weight remains a separate vertical interaction. A solution that puts the guide acceleration into the vertical component equation, or that draws it as a third contact force, has mixed the geometry of the constraint with the force inventory. The corrected diagram makes each role distinct: wall force, weight, and shared horizontal acceleration.

Before numerical substitution, label every equation by its source: an isolated-body component balance, a geometric string relation, a contact condition, or a declared model limit. Those labels expose missing constraints and duplicate equations. If contact is lost, replace the contact condition and its normal-force arrow without rebuilding an unrelated string or system equation.

Treat the diagram as the record of the selected model. Update it before reusing equations when the system boundary, contact state, string tautness, coordinate frame, or applied-force direction changes.

Three-dimensional support contacts.

In three dimensions, a support may restrict motion in one direction while allowing motion in two others, or it may restrict several translations and rotations at once. The free-body diagram should represent only the reactions permitted by the idealized support. A smooth collar on a straight rod can exert force perpendicular to the rod but not along it. A frictionless ball-and-socket joint can exert three force components but no couple moment. A fixed support can exert force components and a reaction couple because it prevents both translation and rotation of the attached body.

These models are not interchangeable. Drawing three force components at a smooth contact that can only push normal to one surface over-constrains the body. Drawing a single normal force at a socket that prevents motion in every direction under- constrains it. The geometry of the support and the allowed motions determine which unknown reactions belong in the diagram. A short note such as “smooth collar” or “pinned joint” carries physical content that an unlabeled point cannot.

Coordinate axes are particularly valuable in three dimensions. Resolve a reaction only into the directions needed by the subsequent equations; an arrow in an oblique direction may be left as a vector until the geometry is clear. Do not add an extra reaction merely because a third axis exists. The number of components follows the support constraint, not the coordinate-system dimension.

Support models fix the allowed reaction components. A smooth collar reacts perpendicular to its guide only, while a pin can react along two independent directions.

A bead slides without friction on a vertical circular wire. At a given point, the wire can push the bead in directions perpendicular to the local wire tangent, but it cannot exert a tangential friction force. A free-body diagram with a single vertical “support force” is incomplete because the contact direction rotates around the wire. A diagram with a tangential reaction would contradict the stated smooth contact model. The correct reaction representation follows the local three- dimensional guide geometry.

Constraint checks and noninertial frames

Every body in a coupled system may use a different positive coordinate. The constraint equation is the place where these choices are reconciled. For a string joining a block on a table to a hanging mass, defining the block positive toward the pulley and the hanging mass positive downward makes their accelerations equal. If both coordinates are defined away from the pulley, the same physical motion gives opposite signed accelerations. Neither convention is preferred; an unstated switch between them is the error.

The sign check starts from the variable string length. Mark each segment that grows when its associated coordinate grows with a plus sign and each segment that shrinks with a minus sign. Differentiate only after the length expression is complete. This method works for pulley systems, rods, rolling constraints, and linked sliders. It also tests whether a supposed constraint remains active: a slack string does not provide a fixed-length equation, and a lost contact no longer links normal motion.

Internal force arrows provide a second sign audit. The tension exerted by a string on each attached body points toward the string segment. Contact forces on two bodies are opposite in direction but need not share a convenient global positive sign. Draw them separately on their own diagrams before applying any cancellation in a combined system. A force cannot be cancelled merely because two arrows look similar; it is internal only when both interacting bodies lie inside the same selected boundary.

A sign audit for a table block joined over a pulley to a hanging mass. Named axes and a string-length relation give the two acceleration signs before any numbers.

Let a table block coordinate increase away from the pulley and let a hanging-mass coordinate increase downward. If the string has one horizontal and one vertical variable segment, its length is $x + y + constant$ . Tautness gives $a_{x} + a_{y} = 0$ . The hanging mass moving downward therefore corresponds to the table block moving toward the pulley, which is negative in this coordinate convention. Writing both accelerations as a positive symbol without this relation would impose a different physical motion from the one drawn.

Noninertial-frame diagram handling.

An accelerating vehicle frame can simplify a constraint because stationary features of the vehicle remain fixed in that coordinate description. The diagram must then make the frame choice explicit. One option is to work in an inertial ground frame: draw only real interactions and write the acceleration required by the vehicle constraint. The other option is to work in the accelerating vehicle frame: draw the same real interactions and include a labelled inertial term associated with the frame acceleration. Either approach can be consistent; combining the two is not.

The two descriptions use different equation forms for the same physical contact. Keeping the frame choice in the record prevents a real wall force from being counted again as a frame term.

Description	Arrows on the block	Acceleration statement
Inertial ground frame	real contact and field interactions only	block acceleration equals the vehicle constraint
Accelerating vehicle frame	same real interactions plus labelled inertial term	block may be stationary in vehicle coordinates
Mixed description	incompatible arrow set	reject before component summation

The inertial term is not a new contact source. It represents the use of an accelerating coordinate frame and acts on every mass in the frame analysis opposite the frame's acceleration. It should be visually distinguished from a normal force, tension, or applied push. The selected system boundary remains important: an inertial term belongs on each mass included in the noninertial analysis, while internal interactions still cancel only for a combined system.

Rotating frames require additional care because their axes change direction. A simple one-dimensional vehicle diagram can often use an accelerating translation model, but a turntable or rotating arm needs rotation-dependent terms and a local axis convention. When the course has not introduced those terms, the safer choice is an inertial frame with time-dependent contact directions rather than an incomplete rotating-frame free-body diagram.

A block remains against the rear wall of a truck accelerating forward. In the ground frame, the wall's normal force accelerates the block forward; the no-separation condition sets the block's forward acceleration equal to the truck's. In the truck frame, the block may be at rest, but the diagram must include a backward inertial term in addition to the forward wall force. Drawing the wall force and setting the acceleration to zero without the inertial term would describe equilibrium in the wrong frame.

Force-inventory diagnostics

When a solution fails a sign or magnitude check, return to the interaction inventory rather than adding arrows until the equations balance. A missing force usually has a missing source: an overlooked rope, a second contact surface, a magnetic field, or an applied support. A double-counted force usually has two names for one interaction, such as both “normal” and “table support,” or it places the action-reaction partner on the same body's diagram. The latter is especially common with strings and blocks in contact.

Use a one-to-one test. For every arrow on the selected body, name the other object or field that exerts it. For every listed interaction, locate exactly one arrow on the selected body. Then inspect the arrow direction against the model: a string pulls, a smooth surface pushes normal to itself, friction lies tangent to contact, and weight points toward the local gravitational source. This test separates a physical omission from a mere component-resolution mistake.

Finally, distinguish forces from constraints and from outcomes. “The block stays on the surface” states a normal-motion condition, not an extra arrow. “The block accelerates with the cart” states a kinematic relation, not a force. “The normal force is zero” can be a solved outcome that changes the contact model. Keeping these three roles separate makes an overloaded diagram easier to repair than an equation list alone.

The inventory can be recorded before component equations are written. The distinction between interaction, constraint, and solved outcome prevents a diagram from acquiring arrows that have no physical source.

Entry	Diagram treatment	Equation role
Contact, string, field, or applied interaction	one arrow on the selected body	force component in $\sum F$
Geometric or no-separation condition	no additional arrow	relation among positions, velocities, or accelerations
Contact loss or slip state	no assumed arrow magnitude	result that may change the active model

Consider a suitcase pulled across a floor by a strap angled upward. An initial diagram contains weight, a vertical normal force, and the strap tension. The horizontal equation appears to predict the observed acceleration, but the calculated normal force has been set equal to weight by habit. The inventory is not missing an arrow; it is missing a component. The upward component of the strap reduces the normal force, so the normal equation must include both weight and that component. If kinetic friction is present, its magnitude changes as a consequence because it depends on the corrected normal force.

Now suppose an extra “reaction to the pull” arrow is drawn backward on the suitcase. That arrow is the suitcase's force on the person or strap, not a second force on the suitcase. It is a double count, and its inclusion would incorrectly cancel part of the genuine strap tension. The corrected diagram has one strap force acting on the suitcase, with its source and direction explicit, followed by component resolution in the selected axes.

A finished solution should state the active contact, string, and frame assumptions in words. “The string remains taut, the block stays in contact with the guide, and the ground frame is used” explains why the selected arrows and constraint equations apply. If later data contradict one of those assumptions, the diagram can be revised at its source instead of patched by adding an unexplained force term. The assumptions should be stated explicitly alongside the final numerical result.