Required practical 3: Determination of g by a freefall method.

The idea

This practical determines the acceleration of free fall, g, by timing a falling object over a measured distance. A common method uses an electromagnet to release a steel ball bearing, which falls through a known height, s, and interrupts a light gate or trapdoor timer. Using s = ut + ½at² with initial velocity u = 0 gives g = 2s/t². Repeating for several heights and plotting s against t² produces a straight line through the origin with gradient ½g, so g is twice the gradient. This reduces random timing error compared with a single measurement.

What earns the marks

• Measure the fall distance s with a metre rule or tape measure, and record the time t with a light gate, trapdoor timer or electronic timer.
• Use the equation s = ut + ½at² with u = 0 to give g = 2s/t² for a single measurement.
• Repeat each height and calculate a mean time to reduce random error.
• Plot a graph of s against t²; the gradient is ½g, so calculate g as twice the gradient.
• Identify and control sources of error, such as parallax when measuring s, delay in manual timing, and air resistance on light objects.
• Compare the experimental value of g with the accepted value, typically about 9.81 m s⁻² near the Earth's surface, and suggest improvements.

Common mistakes and how to put them right

• Using the full fall distance when the timer starts after the object has already fallen.

  Put it right: Measure the distance actually fallen between the release point and the timing gate or trapdoor.

• Forgetting to double the gradient when using an s against t² graph.

  Put it right: Since s = ½gt², the gradient equals ½g, so g = 2 × gradient.

• Timing only one fall and treating it as precise.

  Put it right: Repeat each measurement and use a mean, or use an electronic timer, to reduce random error.

• Assuming air resistance is negligible for all objects.

  Put it right: Use a dense, compact object such as a steel ball bearing to minimise air resistance.

Exam tips

• State the equation you use and show clearly how it rearranges to find g.
• Include units for every measured quantity and for the final value of g.
• Describe how you reduce uncertainty, such as repeating readings, using electronic timing, and measuring from the release point to the timing point.
• When evaluating, refer to specific sources of error and suggest a realistic improvement for each.