M011 · Choose the system. Find its forces.

Free-Body Diagram Builder

Build a force diagram for a crate on a table, on an incline or lifted by a tension-controlled cable. Check the interactions, then release the motion and connect the force sum to acceleration.

Contact regime $\text{Ready}$

Crate / upper acceleration $\text{Ready}$

Floor / surface friction $\text{Ready}$

Selected-system tangential net force $\text{Ready}$

Replay time $\text{Ready}$

Work ledger residual $\text{Ready}$

ISOLATE / PREDICT / RELEASE

Change the interaction. Follow the consequence.

Applied drive / cable tension

F

18.00\,N

Crate mass

m

2.00\,kg

Incline angle

\theta

25.00\,{}^\circ

Apparatus selection

q

0.00\,

Surface static coefficient

\mu_s

0.25\,

Kinetic / static coefficient ratio

r

0.75\,

Gravity

g

9.81\,\frac{\mathrm m}{\mathrm s^2}

All runs start from rest under constant loads. Static friction is whatever equilibrium requires within its bound, not always the maximum. Kinetic coefficients are the corresponding static coefficients times the selected ratio. At equality the solver keeps a feasible sticking contact. Changing controls rebuilds the release from rest.

Crate width 0.8 metres; apparatus lengths share one scale. Ideal guides prevent rotation without translational work. The cable is a constant-tension winch with changing length, not a fixed-length suspension. Stop after 2.4 metres on a plane or 1 metre of cable travel.

Force arrows use one fixed gain of 0.03 metres per newton. All arrows start at a body centre as a translated free-body diagram; they do not show contact pressure or torque application points. The selected pair combines external forces at its mass centre. Gold denotes upper/crate, blue lower, pink contact friction, green drive.

The plots and CSV are calculated model references, not acquired detector data or fitted material measurements. The friction model omits speed dependence, heating feedback, compliance, rolling and microscopic stick-slip. The diagram exercise checks force identification; directions and magnitudes are supplied by the model.

Guided translation; forces and geometry share a consistent Coulomb contact model.

Start with the essentials

Focus question: Which interactions actually act on this object?
One-sentence intuition: A reaction partner acts on the other object, never on this same free body.

Core mathematical model

Balance each body

\sum \vec F_{\mathrm{ext}}=m\vec a

Only interactions on the chosen system belong here.

Static bound, kinetic law

|f_s|\leq\mu_sN,\qquad |f_k|=\mu_kN

Static friction adjusts; sliding friction opposes relative velocity.

Along the incline

ma=F-mg\sin\theta+f

Drive is parallel to the incline; the normal force is perpendicular.

Close the work ledger

W_F+W_g=\Delta K+E_{\mathrm{diss}}

Inter-block loss uses relative displacement, not either block displacement alone.

Common difficulties

A bound is not a prescription

Typical misconceptionStatic friction always equals its maximum.

Better mental modelIt takes the value required by a feasible sticking constraint; only sliding invokes the kinetic magnitude.

Run the experiment

01
Choose a system
Choose the table, incline or cable apparatus.
What to observe: The external-force list follows the system boundary.
02
Predict first
Tap or drag the interaction cards, then check your diagram.
What to observe: A correct diagram need not imply rest.
03
Release and reconcile
Play, pause and scrub the model trajectory.
What to observe: Work, motion and dissipation remain consistent up to the stated travel boundary.