Choose an example at the top: 📐 a box pulled at an angle · ⛰️ lifting a load or pushing it up a ramp · 🛒 the Smart Cart pulled
with a rubber band (class demo) · 🚗 a car braking.
Pick a preset (class demo, slide examples, exit questions) or set the values yourself. Type a value in the box next to a slider and
press Enter.
Press ▶ Start. ◂ / ▸ (or the ← → keys) step through the motion and pause.
The middle column shows the free-body diagram (to scale) and the work done by each force (or a Sankey diagram of where the
energy goes). Forces at 90° to the motion do no work; friction does negative work.
Graphs: the Area tool under an F–s graph gives the work done; under v–t it gives the distance.
The Tangent tool on Ek–s gives the resultant force.
● Record saves a trial; the Data tab plots it (best-fit line through the origin).
Work through the Tasks tab. Write explanations on your worksheet.
The physics
W = Fs cos θ (1 J = 1 N m = 1 kg m² s⁻²)
θ is the angle between the force and the displacement. θ = 90°: no work (normal force, weight on a level floor).
θ = 180°: negative work (friction, brakes).
Variable force: work = area under the F–s graph (spring: W = ½kx²).
Work–energy principle: Wnet = ΔEk = ½mv² − ½mu². Braking: Fbs = ½mu²,
so the braking distance ∝ u²: twice the speed, four times the distance.
Lifting at constant speed: work done = gain in gravitational potential energy mgΔh, whatever the path.
The ramp needs a smaller force over a longer distance (and more work if there is friction).
Model: g = 9.81 N kg⁻¹; friction Ff = μFN (the same μ for starting and sliding); the lift and ramp move at a
constant slow speed (so ΔEk = 0); the Smart Cart pull is fitted to the PASCO lab 07 sample data (0.500 kg, 0.475 J over 0.60 m,
rolling friction 0.03 N).