Known masses give (mass in kg, force in N) readings (0.2, 1.97), (0.3, 2.95), (0.4, 3.92), (0.5, 4.91), (0.6, 5.88). Mass uncertainty is ±0.001 kg and force uncertainty ±0.02 N. (a) Find endpoint gradient and unit. (b) Estimate g. (c) Find percentage uncertainty in the first mass and force. (d) Test whether the intercept is resolved from zero. (e) Explain steepest/shallowest lines and one systematic error.

Question

Accepted Answer

Gradient and g ≈9.78 N/kg; first-reading percentage uncertainties 0.50% and 1.02%; endpoint intercept about 0.015 N, smaller than stated force uncertainty. Endpoint gradient = (5.88 − 1.97)/(0.60 − 0.20) = 3.91/0.40 = 9.775 N kg⁻¹. The unit follows force divided by mass. For F = mg, the best-fit gradient estimates gravitational field strength, so g ≈9.78 N/kg. Agreement with expectation is evidence for calibration, not a reason to replace the measured value. First mass percentage uncertainty is 0.001/0.200 × 100 = 0.50%. Force percentage uncertainty is 0.02/1.97 × 100 = 1.02%, so force resolution contributes the larger fraction. Endpoint-line intercept is 1.97 − 9.775(0.20) = 0.015 N. Since this is smaller than ±0.02 N force uncertainty, the data do not resolve it from zero. Draw steepest and shallowest lines compatible with error bars; half their gradient range estimates uncertainty. A zero offset shifts intercept, whereas mass calibration or force scale error changes gradient.

Force-sensor calibration and uncertainty

What a complete response should do

Force-sensor calibration

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Force-sensor calibration — supplied values
Mass / kg	Force / N
0.2	1.97
0.3	2.95
0.4	3.92
0.5	4.91
0.6	5.88