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.
#
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 the values with the sliders, or type a value in the box next to a slider and press Enter. A value outside the allowed range is set to the nearest allowed value.
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.