Free Body Diagram Builder Physics

θ = 30.0°
m = 2.0 kg
W = 19.6 N
N = 16.97 N
fs,max = 5.09 N
30.0
2.0
0.30

What is the Free Body Diagram Builder?

Quick Answer: A interactive tool to visualise forces acting on a block on an inclined plane. Adjust angle, mass, and friction coefficient. Toggle forces (weight, normal, friction, applied) and see their magnitudes and directions live. Perfect for Newton's laws and equilibrium analysis.

Theory of Inclined Plane Forces

For a block of mass m on a frictionless incline of angle θ, weight W = mg acts downward. Its components are: parallel to plane W∥ = mg sinθ and perpendicular W⊥ = mg cosθ. The normal force N equals W⊥ (if no other vertical forces). Static friction fs opposes relative motion up to fs,max = μs N. If an external force is applied, equilibrium or acceleration can be determined. This tool draws these forces to scale and recalculates in real time.

Step-by-Step Examples

Example 1: Block at Rest

  1. Set θ = 30°, mass 2 kg, μs = 0.3. Weight component down slope is 9.8 N, max static friction 5.09 N < 9.8 N, so block would slide. But we still draw friction (equal to mg sinθ if static?). The tool shows max static friction; actual static friction equals the downslope component if less than max, else motion would occur. We'll draw friction as a force opposing motion up to max.
  2. Increase μs to 0.6 to see friction arrow grow, keeping block static.

Example 2: Adding an Uphill Pull

  1. Enable "Applied Force". A slider for magnitude appears. The force is directed up the incline.
  2. Increase applied force; friction reduces accordingly. When applied force equals mg sinθ, friction becomes zero. Further increase reverses friction direction.

Example 3: Resolving Weight

  1. Toggle "Resolve Weight" to see the weight vector split into perpendicular and parallel components (dashed lines). This clarifies the geometry.

Frequently Asked Questions

How are force lengths determined?

Arrows are drawn to scale (30 px per Newton). Values are shown in the info panel. Very large forces may be clipped.

Why does friction sometimes look shorter than expected?

Friction is self-adjusting: it equals the net external force along the plane (up to μs N). If an applied force is present, friction adjusts to balance it, shown accordingly.

Can I see the equations?

The info panel displays the relevant values: W = mg, N = mg cosθ, fs,max = μs N. The tool does not derive them step-by-step.

Is the block always in equilibrium?

The diagram assumes static equilibrium (no acceleration). If the downslope component exceeds max static friction, the block would slide; we still draw the forces as if static, but you can see that condition in the values.

Can I change the direction of applied force?

Currently applied force is parallel to the incline, direction uphill (positive). You can adjust its magnitude.