Free-Body Diagram Builder
Place an object on an inclined surface with friction and an applied force — all force vectors render live with labeled magnitudes.
Objective
Verify Newton's second law on an inclined surface — observe how weight, normal force, kinetic friction, and an applied force combine into a net force that determines acceleration. The sim models a rigid block on a rigid incline under kinetic friction, ignoring static friction transitions and rotational effects.
Setup
- Set Mass to 5 kg, Incline angle to 20°, Friction coeff. μk to 0.20, and Applied force to 0 N (the defaults). Press Start and let the diagram run for a few seconds.
- Read the six HUD values. Weight (fgOut) should show ≈ 49.05 N; Normal Force (fNOut) ≈ 46.09 N; Friction (ffOut) ≈ 9.22 N; Net Force (fnetOut) ≈ 7.55 N; Acceleration (aOut) ≈ 1.51 m/s².
- Observe the bar chart on the right: Fg is the tallest bar, |Fnet| the shortest. Confirm the weight arrow points straight down and the normal-force arrow points perpendicular to the surface.
- Reset. Set Incline angle to 0° (flat surface). Press Start and confirm Normal Force equals Weight — the ratio FN/Fg should be exactly 1.00.
- Reset again. Increase Applied force to 8 N with angle 20° and μk 0.20. Net Force should drop to ≈ −0.45 N and Acceleration to ≈ 0.09 m/s², demonstrating near-equilibrium.
Analytical Prediction
With mass m = 5 kg, incline θ = 20°, and μk = 0.20 (no applied force), Newton's second law along the surface gives:
The HUD should display Net Force ≈ 7.55 N and Acceleration ≈ 1.51 m/s². On a flat surface (θ = 0°), cos 0° = 1 so FN = Fg exactly.
Results Analysis
After pressing Start with default parameters (m = 5 kg, θ = 20°, μk = 0.20, Fa = 0 N), read all six HUD values. Weight (fgOut) shows 49.05 N; Normal Force (fNOut) ≈ 46.09 N; Friction (ffOut) ≈ 9.22 N; Net Force (fnetOut) ≈ 7.55 N; Acceleration (aOut) ≈ 1.51 m/s². The bar chart shows Fg as the tallest bar and |Fnet| as the shortest — confirming friction and the normal force decomposition. At θ = 0°, FN and Fg match within rounding. Compute the implied mass from the HUD: fnetOut / aOut = 7.55 / 1.51 ≈ 5.00 kg — this confirms Newton's second law is satisfied. Adjust the Applied force slider and watch Net Force update in real time.
Source of Error
This sim models the block as a point mass subject to kinetic friction only — static friction, rolling resistance, and rotational inertia are not modeled. The applied force is constrained to act along the incline surface; oblique applied forces with a normal component are omitted. The sim assumes the block always moves downhill, so the friction direction is fixed uphill regardless of the applied force magnitude — a simplification that breaks down if Fa exceeds Fg∥. These idealizations match the analytical prediction exactly, so any residual difference between prediction and HUD readouts is purely numerical, not physical.
Further Exploration
- Set Friction coeff. μk to 0 and sweep Incline angle from 0° to 60°. Does Net Force grow with sin θ? Compare fnetOut at 30° and 60° — the ratio should be sin 60°/sin 30° ≈ 1.73. Does it?
- With θ = 20° and μk = 0.20, find the Applied force that makes Net Force as close to zero as possible. The prediction gives Fa ≈ 7.55 N — drag the slider and watch the Acceleration readout approach zero.
- Double the mass from 5 kg to 10 kg while keeping θ = 20° and μk = 0.20. Does the Acceleration change? Both Fg and Ff scale with mass, so a = Fnet/m should stay constant — verify this with the aOut readout.
- Set Incline angle to 45° and increase μk from 0 to 0.8 in steps of 0.2. At what friction coefficient does Net Force approach zero? Note that the threshold μk = tan 45° = 1.0 is outside the slider range — what does that tell you about this surface?
- Compare θ = 30° and θ = 60° with μk = 0.30 and Fa = 0. Which angle gives greater acceleration? Are the results symmetric around 45°, and why or why not?