Introduction to CP1: Acceleration of a Freely-Falling Object

Welcome to your first core practical! In this experiment, we are trying to find the value of \(g\)—the acceleration due to gravity. Near the Earth's surface, all objects should fall at the same rate if we ignore air resistance. This value is approximately \(9.81 \text{ m s}^{-2}\).

Understanding how to measure \(g\) is a fundamental skill for Unit 3. It combines your knowledge of kinematics (Unit 1) with practical skills like uncertainty analysis and graphical evaluation.

The Science Behind the Experiment

To measure acceleration, we need to look at the equations of motion (SUVAT). Since we are dropping an object from rest, we can use the following variables:

  • Initial velocity \(u = 0 \text{ m s}^{-1}\)
  • Displacement \(s = h\) (the height from which it is dropped)
  • Acceleration \(a = g\)
  • Time taken \(t\)

We use the equation: \(s = ut + \frac{1}{2}at^{2}\)

Because \(u = 0\), the equation simplifies beautifully to: \(s = \frac{1}{2}gt^{2}\)

Analogy: Imagine dropping a ball from a balcony. The further it falls, the faster it goes. By measuring exactly how long it takes to cover a specific distance, we can "back-calculate" how hard gravity is pulling it down.

Apparatus and Setup

There are two common ways to do this in the lab. Both are designed to measure time very accurately, as humans are often too slow with stopwatches!

1. The Electromagnet and Trapdoor Method:

  • An electromagnet holds a small steel ball.
  • When the power is cut, the ball falls and the timer starts instantly.
  • The ball hits a trapdoor, which breaks the circuit and stops the timer.

2. The Light Gate Method:

  • A "fencing mask" or a simple card is dropped through two light gates.
  • The first gate starts the timer, and the second gate stops it.
  • The distance (\(s\)) is the vertical height between the two gates.

Quick Tip: Use a meter rule to measure the height. Its resolution is usually \(1 \text{ mm}\) or \(0.1 \text{ cm}\). Always measure from the same point (e.g., the bottom of the ball to the top of the trapdoor) to keep your measurements consistent.

Step-by-Step Procedure

  1. Set up the apparatus so the object has a clear vertical path to fall.
  2. Measure the height \(s\) using a meter rule. Check for parallax error by ensuring your eye is level with the measurement.
  3. Drop the object and record the time \(t\) from the data logger or electronic timer.
  4. Repeat the measurement for the same height at least three times and calculate a mean time. This reduces the effect of random errors.
  5. Change the height \(s\) and repeat the process for at least six different heights.

Processing the Results

To find a reliable value for \(g\), we don't just use one calculation; we plot a graph! If we compare our equation \(s = \frac{1}{2}gt^{2}\) to the equation for a straight line \(y = mx + c\):

  • Plot \(s\) on the y-axis.
  • Plot \(t^{2}\) on the x-axis.
  • The gradient (\(m\)) of the line will be \(\frac{1}{2}g\).

Therefore, \(g = 2 \times \text{gradient}\).

Important Graphing Rule: When calculating the gradient, always draw a large triangle on your line of best fit. This reduces the percentage uncertainty in your gradient calculation.

Dealing with Uncertainties and Errors

In your exam, you might be asked to criticise an experiment or suggest improvements. Here is what to look out for:

  • Air Resistance: This is a systematic error. It acts upwards, reducing the resultant acceleration. To minimize this, use a small, heavy object (like a steel ball) rather than something light like a feather.
  • Reaction Time: If a student uses a manual stopwatch, the uncertainty in time is much larger. Using electronic timers or light gates eliminates this problem.
  • Zero Errors: Check that your ruler starts at \(0\) and your timer is reset before every drop.
  • Parallax Error: Not looking at the ruler at eye level. This can be fixed by using a set square to align the ball with the ruler.

Did you know? If your line of best fit doesn't pass through the origin \((0,0)\) even though the physics says it should, it's a strong sign of a systematic error in your measurements!

Key Takeaways for Revision

  • The Formula: \(s = \frac{1}{2}gt^{2}\) (derived from SUVAT where \(u=0\)).
  • The Graph: Plot \(s\) against \(t^{2}\). \(g = 2 \times \text{gradient}\).
  • Precision: Use light gates or electromagnets to avoid human reaction time.
  • Repeatability: Always take repeat readings to identify anomalies and calculate a mean.
  • Data Sheet: Remember that on your Edexcel data sheet, \(g\) is given as \(9.81 \text{ m s}^{-2}\). Compare your experimental value to this to judge accuracy.

Quick Review: If your graph of \(s\) vs \(t^{2}\) has a gradient of \(4.80\), what is your experimental value for \(g\)?
(Answer: \(2 \times 4.80 = 9.60 \text{ m s}^{-2}\)).

Don't worry if this seems like a lot of steps! Just remember: measure distance and time, use the SUVAT equations, and use a graph to find the average behavior of your falling object.