The method and the results are on the gravitational field lab. Do the analysis yourself first, then check the answers below.
Quick answer: Newton's law of gravitation says two masses attract with force F = G m₁m₂/r². These answers go with the Physics 11-12 lab on gravitational field: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
The answers use the sample results in the table, so your own values will differ slightly. Check that you divided the frame count by 240 to get seconds and that you squared the time before calculating g.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.1
Question 1 Time from frames
t = 118 ÷ 240 = 0.492 s. The ball is released without a push, so the initial velocity is zero, and s = ½ g t² applies.t = 0.492 s.
Question 2 Value of g
g = 2 h ÷ t² = 2 × 0.40 ÷ (68 ÷ 240)² = 0.80 ÷ 0.0803 = 9.97 m/s².g = 9.97 m/s².
Question 3 Mean value
Mean g = (9.97 + 9.79 + 9.93 + 9.68 + 9.84) ÷ 5 = 9.84 m/s². The difference is (9.84 − 9.81) ÷ 9.81 × 100 % = 0.3 %.mean g = 9.84 m/s².
Question 4 Graph
Since h = ½ g t², plot h on the y-axis and t² on the x-axis. The graph is a straight line through the origin with gradient ½ g. The gradient of the best fit through the origin here is 4.90 m/s², giving g = 9.81 m/s².g = 2 × gradient = 9.81 m/s².
Question 5 Field strength and the Earth
M = g R² ÷ G = 9.81 × (6.37 × 10⁶)² ÷ 6.67 × 10⁻¹¹ = 9.81 × 4.058 × 10¹³ ÷ 6.67 × 10⁻¹¹ = 5.97 × 10²⁴ kg. With your gradient value g = 9.81 the mass is 5.97e+24 kg.M = 5.97 × 10²⁴ kg.
Question 6 Uncertainty in frames
The uncertainty in t is 1 ÷ 68 = 1.5 %. Since g ∝ 1/t², the uncertainty in g is 2 × 1.5 % = 2.9 %, about ±0.3 m/s². The longer drops have smaller uncertainties, for example 2 × 1 ÷ 153 = 1.3 % for 2.00 m.±2.9 %.
Question 7 Air resistance
Air resistance reduces the acceleration, so the time is slightly longer and the calculated g slightly smaller. For a dense steel ball moving below 6 m/s, the drag is much smaller than the weight, so the effect is under 1 %.g is slightly underestimated.
Question 8 Improvements
Use a light gate or electromagnet release with a digital timer instead of counting frames, and repeat each height three times to average the results. Film perpendicular to the wall to avoid parallax errors in reading the release frame.use electronic timing and repeat the drops.
