In an experiment to investigate the relationship between force and acceleration a student applied a force to a body and measured the resulting acceleration - Leaving Cert Physics - Question 1 - 2005

The applied force was measured using a Newton balance or a force sensor. The student would:

1. Ensure the force sensor is calibrated correctly.
2. Attach weights to the trolley or apply a known force using weights.
3. Read the force directly from the balance or sensor, ensuring the appropriate units (Newton) are used.

To plot the graph:

1. Label the X-axis as 'Acceleration (m/s²)' and the Y-axis as 'Force (N)'.
2. Mark three points based on the given data from the table:
   • (0.10, 0.1)
   • (0.22, 0.2)
   • (0.32, 0.3)
3. Plot additional points to ensure a clear trend such as (0.44, 0.4), (0.55, 0.5), (0.65, 0.6), and (0.76, 0.7).
4. Ensure you plot these points clearly and draw a line of best fit that best represents the data. If the graph is neat and well labeled, it will be easier to interpret.

To calculate the slope of the graph, use two points on the line of best fit. The slope ( ext{slope}) can be calculated by:

$ext{slope} = \frac{\Delta y}{\Delta x} = \frac{F_2 - F_1}{a_2 - a_1}$

For example, using points (0.55, 0.5) and (0.65, 0.6):

1. Calculate the rise: $0.6 - 0.5 = 0.1$
2. Calculate the run: $0.65 - 0.55 = 0.1$
3. $\text{slope} = \frac{0.1}{0.1} = 1.0 N/(m/s²)$

To find the mass ( ext{m}) of the body, use Newton's second law, $F = ma$:

$m = \frac{F}{a}$

For the value determined from the slope, this indicates that for 1N of force, the body accelerates at 1 m/s², hence:

$m = 1 ext{ kg}$

One valid precaution the student could take is:

• Ensure that the track is level and smooth to reduce friction, which could skew the results. Alternatively, the student could also secure the trolley to prevent it from leaving the track during the experiment.