A trolley is pulled horizontally. The recorded pairs (applied force in N, acceleration in m/s²) are (0.8, 0), (1.2, 0), (1.6, 0.5), (2.0, 1.0), (2.4, 1.5). (a) Describe the pattern and identify the force needed before sustained motion appears. [3] (b) For the moving points, use F = ma + f to determine the trolley mass m and the approximately constant friction f. [5] (c) Assess whether all five readings support one straight-line model. [2] (d) Propose one improvement that would test the model more rigorously. [2]

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The stationary readings show a threshold up to about 1.2 N. For the moving data Δa/ΔF = 1.25 kg⁻¹, so m = 0.80 kg and f = 1.20 N. Static and moving behaviour should not be forced onto one line. (a) Acceleration remains zero at 0.8 N and 1.2 N, then rises by 0.5 m/s² for each further 0.4 N. Sustained motion begins only above an applied force of about 1.2 N. (b) For moving points, a = (F − f)/m, so the gradient of acceleration against force is 1/m. Gradient = (1.5 − 0.5)/(2.4 − 1.6) = 1.25 kg⁻¹. (b) Therefore m = 1/1.25 = 0.80 kg. Substituting F = 1.6 N and a = 0.5 m/s² gives f = F − ma = 1.6 − 0.80 × 0.5 = 1.20 N. (c) The three moving readings fit F = 0.80a + 1.20 exactly, but the two zero-acceleration readings represent adjustable static friction. They are not evidence that the same kinetic straight line extends to rest. (d) Add closely spaced force values around 1.2–1.6 N and repeat each measurement. A force sensor and motion sensor would show both the breakaway peak and the steadier force while moving.

Extract mass and friction from acceleration data

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Applied force and trolley acceleration

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