Top: the acceleration for every hanging mass m2 (up the slope +). In the green band
static friction holds the system at rest. Bottom: the velocity after ▶ Release — the gradient is a.
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Surface
θ / °
m1 / kg
m2 / kg
a / m s⁻²
T / N
m2g / N
How to use this simulation
Choose the surfaces, the block mass m₁, the hanging mass m₂ and the ramp angle
(θ = 0° is a flat bench, like the Smart Cart demo).
Set each value with ▼ and ▲ (hold to go faster; the ↑ ↓ keys or the mouse wheel in the box also work, Shift = ×10), or type a value in the box. ↺ puts it back to its start value. Outside the classroom range the box turns amber ⚠: fine to explore, but the lab can't do this.
Move the pointer over any graph (or tap it): a dashed line shows the values where it cuts each curve, or the values of the nearest data point.
The block is held at the start. Press ▶ Release. If static friction can hold it, nothing moves;
otherwise the system accelerates until the block has moved 0.25 m.
Press ● Record after a run. The Data & analysis tab plots a against the tension T.
Work through the Tasks tab and write explanations on your worksheet.
The physics (Newton's 2nd law — Blocks 3–4)
Take "m₂ falls, block moves up the slope" as positive.
Hanging mass: m₂g − T = m₂a. Block: T − m₁g sin θ − Ff = m₁a.
Add them (the tensions cancel): a = (m₂g − m₁g sin θ − Ff) / (m₁ + m₂), with Ff = μdm₁g cos θ against the motion.
At rest the forces balance; static friction can hold it while m₁(sin θ − μs cos θ) ≤ m₂ ≤ m₁(sin θ + μs cos θ).
While accelerating, T = m₂(g − a) is less than m₂g.
Model: light string, frictionless pulley, the block moves at most 0.25 m; μ values are typical classroom values. "Smart Cart wheels"
gives the 0.035 N rolling friction of the Block 3 demo for a 0.500 kg cart.
Newton's laws
The badge above the scene says which law applies at this moment: 1st law — at rest or moving at a constant velocity, the resultant force is zero (ΣF = 0); 2nd law — accelerating, ΣF = ma. The table under the free-body diagram adds up the forces (ΣF) and compares them with m a (▾ folds it). Tick 3rd-law pairs to see every force with its partner: the same size and type, in the opposite direction, acting on the other body (the Earth, the floor, the string, the fluid…).